Step-by-Step Guidance for College Algebra Exam Review

{"type":"doc","content":[{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q1. Solve the equation using the multiplication property of equality. Be sure to check your solution."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Solving Linear Equations"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to solve a linear equation using the multiplication property of equality and to check your solution."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Multiplication Property of Equality: If "},{"type":"inlineMath","attrs":{"latex":"a = b"}},{"type":"text","text":", then "},{"type":"inlineMath","attrs":{"latex":"a \\cdot c = b \\cdot c"}},{"type":"text","text":" for any "},{"type":"inlineMath","attrs":{"latex":"c \\neq 0"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Linear Equation: An equation of the form "},{"type":"inlineMath","attrs":{"latex":"ax + b = c"}},{"type":"text","text":"."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify the equation and isolate the variable on one side."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use the multiplication property of equality to eliminate fractions or coefficients."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Simplify both sides of the equation as needed."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Check your solution by substituting the value back into the original equation."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_1.png","alt":"Handwritten solution for linear equation","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"x = -15"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"By isolating "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":" and checking the solution, you confirm the answer is correct."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q2. Solve the equation. Check your solution."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Solving Linear Equations with Variables on Both Sides"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to solve equations where variables appear on both sides and to check your solution."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Combine like terms: Group terms with the same variable."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Linear Equation: "},{"type":"inlineMath","attrs":{"latex":"ax + b = cx + d"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Expand and simplify both sides of the equation."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Move all terms with the variable to one side and constants to the other."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Combine like terms and solve for the variable."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Check your solution by substituting back into the original equation."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_1.png","alt":"Handwritten solution for linear equation with variables on both sides","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"k = 0"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"After simplifying and checking, you find the solution is "},{"type":"inlineMath","attrs":{"latex":"k = 0"}},{"type":"text","text":"."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q3. Solve the equation. Check your solution."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Solving Linear Equations with Fractions"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to solve equations involving fractions and to check your solution."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Clear fractions by multiplying both sides by the least common denominator (LCD)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Linear Equation: "},{"type":"inlineMath","attrs":{"latex":"\\frac{a}{b}x + c = d"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify the LCD and multiply both sides to clear fractions."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Simplify the resulting equation."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Isolate the variable and solve."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Check your solution by substituting back into the original equation."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_1.png","alt":"Handwritten solution for linear equation with fractions","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"x = 6"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Multiplying by the LCD and checking confirms the solution."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q4. Solve the equation. Check your solution."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Solving Linear Equations with Decimals"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to solve equations involving decimals and to check your solution."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Linear Equation: "},{"type":"inlineMath","attrs":{"latex":"ax + b = cx + d"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Combine like terms and isolate the variable."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Expand and simplify both sides of the equation."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Move all terms with the variable to one side and constants to the other."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Combine like terms and solve for the variable."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Check your solution by substituting back into the original equation."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_1.png","alt":"Handwritten solution for linear equation with decimals","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"z = -8"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"After simplifying and checking, you find the solution is "},{"type":"inlineMath","attrs":{"latex":"z = -8"}},{"type":"text","text":"."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q5. Solve the equation. State whether the equation is a contradiction, an identity, or a conditional equation."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Types of Equations (Contradiction, Identity, Conditional)"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to solve an equation and classify it as a contradiction, identity, or conditional equation."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Contradiction: No solution exists."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identity: All real numbers are solutions."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Conditional: Only certain values are solutions."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Simplify both sides of the equation."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Compare the resulting expressions to see if they are always equal, never equal, or equal for specific values."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Classify the equation based on your findings."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_1.png","alt":"Handwritten solution for equation classification","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: Contradiction"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The equation simplifies to a false statement, so it is a contradiction."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q6. Solve the equation. State whether the equation is a contradiction, an identity, or a conditional equation."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Types of Equations (Contradiction, Identity, Conditional)"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to solve an equation and classify it as a contradiction, identity, or conditional equation."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Contradiction: No solution exists."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identity: All real numbers are solutions."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Conditional: Only certain values are solutions."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Simplify both sides of the equation."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Compare the resulting expressions to see if they are always equal, never equal, or equal for specific values."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Classify the equation based on your findings."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_2.png","alt":"Handwritten solution for equation classification","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: Identity"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The equation simplifies to a true statement for all values, so it is an identity."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q7. Solve for y in the equation "},{"type":"inlineMath","attrs":{"latex":"9x - 3y = 6"}},{"type":"text","marks":[{"type":"bold"}],"text":"."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Solving for a Variable (Rewriting Equations)"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to solve for a specific variable in a linear equation."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Isolate the variable: Move all terms involving the variable to one side."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Linear Equation: "},{"type":"inlineMath","attrs":{"latex":"ax + by = c"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Subtract "},{"type":"inlineMath","attrs":{"latex":"9x"}},{"type":"text","text":" from both sides to isolate "},{"type":"inlineMath","attrs":{"latex":"-3y"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Divide both sides by "},{"type":"inlineMath","attrs":{"latex":"-3"}},{"type":"text","text":" to solve for "},{"type":"inlineMath","attrs":{"latex":"y"}},{"type":"text","text":"."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_2.png","alt":"Handwritten solution for solving for y","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"y = 3x - 2"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"After isolating "},{"type":"inlineMath","attrs":{"latex":"y"}},{"type":"text","text":", you rewrite the equation in terms of "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":"."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q8. Simple Interest: "},{"type":"inlineMath","attrs":{"latex":"I = Prt"}},{"type":"text","marks":[{"type":"bold"}],"text":". Solve for "},{"type":"inlineMath","attrs":{"latex":"r"}},{"type":"text","marks":[{"type":"bold"}],"text":" and find $r$ when "},{"type":"inlineMath","attrs":{"latex":"I = 350"}},{"type":"text","marks":[{"type":"bold"}],"text":", "},{"type":"inlineMath","attrs":{"latex":"P = 2000"}},{"type":"text","marks":[{"type":"bold"}],"text":", "},{"type":"inlineMath","attrs":{"latex":"t = 2.5"}},{"type":"text","marks":[{"type":"bold"}],"text":" years."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Simple Interest Formula"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to manipulate formulas and substitute values."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Simple Interest: "},{"type":"inlineMath","attrs":{"latex":"I = Prt"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Solving for "},{"type":"inlineMath","attrs":{"latex":"r"}},{"type":"text","text":": "},{"type":"inlineMath","attrs":{"latex":"r = \\frac{I}{Pt}"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Rewrite the formula to solve for "},{"type":"inlineMath","attrs":{"latex":"r"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Substitute the given values for "},{"type":"inlineMath","attrs":{"latex":"I"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"P"}},{"type":"text","text":", and "},{"type":"inlineMath","attrs":{"latex":"t"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the calculation for "},{"type":"inlineMath","attrs":{"latex":"r"}},{"type":"text","text":"."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_2.png","alt":"Handwritten solution for simple interest","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"r = 0.07"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Substituting the values gives the interest rate."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q9. Translate the statement into an equation. Let "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","marks":[{"type":"bold"}],"text":" represent the unknown number. Do not solve."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Translating Verbal Statements to Algebraic Equations"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to convert a word problem into an algebraic equation."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Triple: Multiply by 3."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Sum: Addition."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify the unknown number as "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Translate \"triple the sum of a number and 7\" as "},{"type":"inlineMath","attrs":{"latex":"3(x + 7)"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Translate \"4 more than the number\" as "},{"type":"inlineMath","attrs":{"latex":"x + 4"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the equation: "},{"type":"inlineMath","attrs":{"latex":"3(x + 7) = x + 4"}},{"type":"text","text":"."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try writing the equation before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"3(x + 7) = x + 4"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This equation represents the statement mathematically."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q10. A 59-inch piece of wire is to be cut into three pieces. The shortest piece is 5 inches shorter than the middle piece and the longest piece is 4 inches longer than the middle piece. How long is each piece?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Translating Word Problems to Equations"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to model a real-world situation with an equation."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Let "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":" be the length of the middle piece."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Shortest piece: "},{"type":"inlineMath","attrs":{"latex":"x - 5"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Longest piece: "},{"type":"inlineMath","attrs":{"latex":"x + 4"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Total length: "},{"type":"inlineMath","attrs":{"latex":"x + (x - 5) + (x + 4) = 59"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Assign "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":" to the middle piece."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Express the other pieces in terms of "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Write the equation for the total length."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Simplify the equation before solving."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try setting up the equation before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_3.png","alt":"Handwritten solution for wire cutting problem","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: Middle piece = 20 inches, Shortest = 15 inches, Longest = 24 inches"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Solving the equation gives the lengths of each piece."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q11. After Mrs. Fisher lost 7% of her investment, she had $20,925. What was Mrs. Fisher's original investment?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Percent Decrease and Algebraic Modeling"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to model a percent decrease and solve for the original value."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Let "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":" be the original investment."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"After losing 7%, she has "},{"type":"inlineMath","attrs":{"latex":"0.93x = 20,925"}},{"type":"text","text":"."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the equation for the remaining investment."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Isolate "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":" by dividing both sides by "},{"type":"inlineMath","attrs":{"latex":"0.93"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the calculation for "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":"."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try setting up the equation before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_3.png","alt":"Handwritten solution for percent decrease problem","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"x = 22,500"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Dividing by "},{"type":"inlineMath","attrs":{"latex":"0.93"}},{"type":"text","text":" gives the original investment."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q12. The length of a rectangle is 8 feet longer than the width. If the perimeter is 116 feet, find the length and width."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Perimeter of a Rectangle"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to use the perimeter formula and solve for unknowns."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Perimeter: "},{"type":"inlineMath","attrs":{"latex":"P = 2(l + w)"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Length: "},{"type":"inlineMath","attrs":{"latex":"l = w + 8"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Perimeter: "},{"type":"inlineMath","attrs":{"latex":"116 = 2(w + w + 8)"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Express length in terms of width."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Substitute into the perimeter formula."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Simplify and solve for "},{"type":"inlineMath","attrs":{"latex":"w"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Find "},{"type":"inlineMath","attrs":{"latex":"l"}},{"type":"text","text":" using "},{"type":"inlineMath","attrs":{"latex":"w"}},{"type":"text","text":"."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try setting up the equation before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_3.png","alt":"Handwritten solution for rectangle perimeter problem","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: Width = 25 ft, Length = 33 ft"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Solving gives the dimensions of the rectangle."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q13. Two boats leave a port at the same time, one going north and the other south. The northbound boat travels 18 mph faster than the southbound boat. If the southbound boat is traveling at 43 mph, how long will it be before they are 1352 miles apart?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Distance, Rate, and Time"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to use the formula "},{"type":"inlineMath","attrs":{"latex":"D = rt"}},{"type":"text","text":" for combined rates."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Distance formula: "},{"type":"inlineMath","attrs":{"latex":"D = r_1t + r_2t"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Northbound rate: "},{"type":"inlineMath","attrs":{"latex":"43 + 18 = 61"}},{"type":"text","text":" mph"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Southbound rate: $43$ mph"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Total distance: $1352$ miles"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the equation: "},{"type":"inlineMath","attrs":{"latex":"61t + 43t = 1352"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Combine rates: "},{"type":"inlineMath","attrs":{"latex":"104t = 1352"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Solve for "},{"type":"inlineMath","attrs":{"latex":"t"}},{"type":"text","text":"."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try setting up the equation before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_3.png","alt":"Handwritten solution for boat distance problem","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"t = 13"}},{"type":"text","marks":[{"type":"bold"}],"text":" hours"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Dividing gives the time until the boats are 1352 miles apart."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q14. Solve the inequality and express the solution set in set-builder notation and interval notation. Graph the solution set on the real number line."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Solving Linear Inequalities"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to solve inequalities and represent the solution graphically and in notation."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Linear Inequality: "},{"type":"inlineMath","attrs":{"latex":"ax + b < cx + d"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set-builder notation: "},{"type":"inlineMath","attrs":{"latex":"{x | x > a}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Interval notation: "},{"type":"inlineMath","attrs":{"latex":"(a, \\infty)"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Simplify both sides of the inequality."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Isolate the variable on one side."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Express the solution in set-builder and interval notation."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Graph the solution on the real number line."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_4.png","alt":"Handwritten solution and graph for linear inequality","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"n > 8"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set-builder: "},{"type":"inlineMath","attrs":{"latex":"{n | n > 8}"}},{"type":"text","text":"; Interval: "},{"type":"inlineMath","attrs":{"latex":"(8, \\infty)"}}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q15. Solve the inequality and express the solution set in set-builder notation and interval notation. Graph the solution set on the real number line."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Solving Linear Inequalities"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to solve inequalities and represent the solution graphically and in notation."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Linear Inequality: "},{"type":"inlineMath","attrs":{"latex":"ax + b < cx + d"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set-builder notation: "},{"type":"inlineMath","attrs":{"latex":"{x | x > a}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Interval notation: "},{"type":"inlineMath","attrs":{"latex":"(a, \\infty)"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Simplify both sides of the inequality."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Isolate the variable on one side."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Express the solution in set-builder and interval notation."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Graph the solution on the real number line."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_5.png","alt":"Handwritten solution and graph for linear inequality","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"y < -7"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set-builder: "},{"type":"inlineMath","attrs":{"latex":"{y | y < -7}"}},{"type":"text","text":"; Interval: "},{"type":"inlineMath","attrs":{"latex":"(-\\infty, -7)"}}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q16. Graph the linear equation by finding its intercepts: "},{"type":"inlineMath","attrs":{"latex":"2x + 4y = 16"}},{"type":"text","marks":[{"type":"bold"}],"text":"."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Graphing Linear Equations Using Intercepts"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to find intercepts and graph a line."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"x-intercept: Set "},{"type":"inlineMath","attrs":{"latex":"y = 0"}},{"type":"text","text":" and solve for "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"y-intercept: Set "},{"type":"inlineMath","attrs":{"latex":"x = 0"}},{"type":"text","text":" and solve for "},{"type":"inlineMath","attrs":{"latex":"y"}},{"type":"text","text":"."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Find the x-intercept by setting "},{"type":"inlineMath","attrs":{"latex":"y = 0"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Find the y-intercept by setting "},{"type":"inlineMath","attrs":{"latex":"x = 0"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Plot both intercepts on the graph."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Draw the line through the intercepts."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try graphing before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_5.png","alt":"Handwritten graph for linear equation","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: x-intercept = 8, y-intercept = 4"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The line passes through (8, 0) and (0, 4)."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q17. Plot the points (2, -6) and (-2, -2) in a rectangular coordinate system, draw a line through the points, and find and interpret the slope."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Slope of a Line"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to plot points, draw a line, and calculate slope."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Slope formula: "},{"type":"inlineMath","attrs":{"latex":"m = \\frac{y_2 - y_1}{x_2 - x_1}"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Plot the points (2, -6) and (-2, -2) on the coordinate plane."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Draw a line through both points."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate the slope using the formula."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Interpret the slope: How does "},{"type":"inlineMath","attrs":{"latex":"y"}},{"type":"text","text":" change as "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":" increases?"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try calculating the slope before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_6.png","alt":"Handwritten graph and slope calculation","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: Slope = -1"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For each increase of 1 in "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"y"}},{"type":"text","text":" decreases by 1."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q18. Find any two ordered pairs that lie on the given line "},{"type":"inlineMath","attrs":{"latex":"5x + y = -1"}},{"type":"text","marks":[{"type":"bold"}],"text":". Graph the line and determine the slope."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Finding Points and Slope of a Line"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to find points on a line, graph it, and determine the slope."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Choose values for "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":" and solve for "},{"type":"inlineMath","attrs":{"latex":"y"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Slope formula: "},{"type":"inlineMath","attrs":{"latex":"m = \\frac{y_2 - y_1}{x_2 - x_1}"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Choose two values for "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":" and solve for "},{"type":"inlineMath","attrs":{"latex":"y"}},{"type":"text","text":" to get ordered pairs."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Plot the points and draw the line."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate the slope using the formula."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try finding the points and slope before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_6.png","alt":"Handwritten graph and slope calculation for line","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: Slope = -5"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The slope is calculated from the points found."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q19. Find the slope and y-intercept of the line whose equation is "},{"type":"inlineMath","attrs":{"latex":"x - 4y = 8"}},{"type":"text","marks":[{"type":"bold"}],"text":"."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Slope and y-intercept from Standard Form"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to rewrite an equation in slope-intercept form and identify slope and y-intercept."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Slope-intercept form: "},{"type":"inlineMath","attrs":{"latex":"y = mx + b"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Slope: "},{"type":"inlineMath","attrs":{"latex":"m"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"y-intercept: "},{"type":"inlineMath","attrs":{"latex":"b"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Rewrite the equation in slope-intercept form."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify the slope and y-intercept from the equation."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try rewriting the equation before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_7.png","alt":"Handwritten slope and y-intercept calculation","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: Slope = 1/4, y-intercept = -2"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Rewriting gives "},{"type":"inlineMath","attrs":{"latex":"y = \\frac{1}{4}x - 2"}},{"type":"text","text":"."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q20. Use the slope and y-intercept to graph the line whose equation is "},{"type":"inlineMath","attrs":{"latex":"y = -\\frac{5}{3}x - 2"}},{"type":"text","marks":[{"type":"bold"}],"text":"."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Graphing Using Slope and y-intercept"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to graph a line using its slope and y-intercept."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Slope: "},{"type":"inlineMath","attrs":{"latex":"m = -\\frac{5}{3}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"y-intercept: "},{"type":"inlineMath","attrs":{"latex":"b = -2"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Plot the y-intercept at (0, -2)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use the slope to find another point: down 5, right 3."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Draw the line through the points."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try graphing before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_7.png","alt":"Handwritten graph for slope and y-intercept","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: Line passes through (0, -2) with slope -5/3"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Graphing uses the y-intercept and slope."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q21. Find the equation of the line with the slope undefined and the x-intercept (-5, 0)."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Vertical Lines and x-intercepts"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to write the equation of a vertical line."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Vertical line: "},{"type":"inlineMath","attrs":{"latex":"x = a"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Slope is undefined."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Recognize that a vertical line has an equation "},{"type":"inlineMath","attrs":{"latex":"x = a"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use the x-intercept to write the equation."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try writing the equation before revealing the answer!"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/beginning-intermediate-algebra/sub_images/c80ba322_image_7.png","alt":"Handwritten equation for vertical line","title":null,"width":null,"height":null}}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"x = -5"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The equation of the vertical line is "},{"type":"inlineMath","attrs":{"latex":"x = -5"}},{"type":"text","text":"."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bo