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Add like terms in the expression: "},{"type":"inlineMath","attrs":{"latex":"3x - 2y - x + 5 - 7 + 4y + 2x - 2"}}]},{"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: Combining Like Terms"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to identify and combine like terms in an algebraic expression."}]},{"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":"Like Terms: Terms that have the same variable raised to the same power."}]}]}]},{"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":"Group all "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":" terms together: "},{"type":"inlineMath","attrs":{"latex":"3x"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"-x"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"2x"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Group all "},{"type":"inlineMath","attrs":{"latex":"y"}},{"type":"text","text":" terms together: "},{"type":"inlineMath","attrs":{"latex":"-2y"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"4y"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Group all constant terms together: $5"},{"type":"inlineMath","attrs":{"latex":", "}},{"type":"text","text":"-7$, $-2$."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Add the coefficients for each group to combine like terms."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own 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":"4x + 2y - 4"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Combine "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":" terms: "},{"type":"inlineMath","attrs":{"latex":"3x - x + 2x = 4x"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Combine "},{"type":"inlineMath","attrs":{"latex":"y"}},{"type":"text","text":" terms: "},{"type":"inlineMath","attrs":{"latex":"-2y + 4y = 2y"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Combine constants: "},{"type":"inlineMath","attrs":{"latex":"5 - 7 - 2 = -4"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"So, the simplified expression is "},{"type":"inlineMath","attrs":{"latex":"4x + 2y - 4"}},{"type":"text","text":"."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q3. 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Determine if the system is dependent, independent, or inconsistent: "},{"type":"inlineMath","attrs":{"latex":"\\begin{cases}2x - 3y = 7 \\\\ 6x - 9y = 10\\end{cases}"}}]},{"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: Systems of Linear Equations"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to classify a system by comparing the ratios of coefficients and constants."}]},{"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":"Dependent: Infinite solutions (same line)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Independent: One solution (intersecting lines)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Inconsistent: No solution (parallel lines)."}]}]}]},{"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":"Multiply the first equation by $3$ and compare to the second equation."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Check if the left sides are proportional but the right sides are not."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"If so, the system is inconsistent."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: Inconsistent"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The left sides are proportional, but the right sides are not, so the system is inconsistent (no solution)."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q18. Determine if the system is dependent, independent, or inconsistent: "},{"type":"inlineMath","attrs":{"latex":"\\begin{cases}2x - 3y = 7 \\\\ 6x + 9y = 21\\end{cases}"}}]},{"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: Systems of Linear Equations"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to classify a system by comparing the ratios of coefficients and constants."}]},{"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":"Dependent: Infinite solutions (same line)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Independent: One solution (intersecting lines)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Inconsistent: No solution (parallel lines)."}]}]}]},{"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":"Compare the ratios of coefficients for "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":" and "},{"type":"inlineMath","attrs":{"latex":"y"}},{"type":"text","text":" in both equations."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"If the ratios are not equal, the lines intersect at one point (independent)."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: Independent"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The ratios are not equal, so the system is independent (one solution)."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q19. Substitute "},{"type":"inlineMath","attrs":{"latex":"y = 3"}},{"type":"text","marks":[{"type":"bold"}],"text":" into the equation "},{"type":"inlineMath","attrs":{"latex":"2x - 5y = 11"}}]},{"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: Substitution in Linear Equations"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to substitute a value for a variable and solve for the other variable."}]},{"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":"Substitution: Replace "},{"type":"inlineMath","attrs":{"latex":"y"}},{"type":"text","text":" with $3$ in the equation."}]}]}]},{"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":"Replace "},{"type":"inlineMath","attrs":{"latex":"y"}},{"type":"text","text":" with $3"},{"type":"inlineMath","attrs":{"latex":" in the equation: $2x - 5(3) = 11"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Multiply "},{"type":"inlineMath","attrs":{"latex":"-5"}},{"type":"text","text":" by $3$."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Add $15"},{"type":"inlineMath","attrs":{"latex":" to both sides to solve for "}},{"type":"text","text":"x$."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Divide both sides by $2"},{"type":"inlineMath","attrs":{"latex":" to find "}},{"type":"text","text":"x$."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own 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":"x = 13"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Substitute and solve: "},{"type":"inlineMath","attrs":{"latex":"2x - 15 = 11 \\Rightarrow 2x = 26 \\Rightarrow x = 13"}},{"type":"text","text":"."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q20. Solve the system of equations: "},{"type":"inlineMath","attrs":{"latex":"\\begin{cases}x - 3y = -5 \\\\ y = 4\\end{cases}"}}]},{"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 Systems by Substitution"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to solve a system of equations using substitution."}]},{"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":"Substitute the value of "},{"type":"inlineMath","attrs":{"latex":"y"}},{"type":"text","text":" into the first equation to solve for "},{"type":"inlineMath","attrs":{"latex":"x"}},{"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":"Substitute "},{"type":"inlineMath","attrs":{"latex":"y = 4"}},{"type":"text","text":" into the first equation: "},{"type":"inlineMath","attrs":{"latex":"x - 3(4) = -5"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Multiply "},{"type":"inlineMath","attrs":{"latex":"-3"}},{"type":"text","text":" by $4$."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Add $12"},{"type":"inlineMath","attrs":{"latex":" to both sides to solve for "}},{"type":"text","text":"x$."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own 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":"x = 7"}},{"type":"text","marks":[{"type":"bold"}],"text":", "},{"type":"inlineMath","attrs":{"latex":"y = 4"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Substitute and solve: "},{"type":"inlineMath","attrs":{"latex":"x - 12 = -5 \\Rightarrow x = 7"}},{"type":"text","text":"."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q21. Solve the 1st order equation: "},{"type":"inlineMath","attrs":{"latex":"3(x - 1) + 2(3x - 5) = 5(2x + 3)"}}]},{"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 Distribution"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to use the distributive property and combine like terms to solve for "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":"."}]},{"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":"Distributive Property: "},{"type":"inlineMath","attrs":{"latex":"a(b + c) = ab + ac"}}]}]}]},{"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":"Distribute $3"},{"type":"inlineMath","attrs":{"latex":" to "}},{"type":"text","text":"(x - 1)"},{"type":"inlineMath","attrs":{"latex":", $2"}},{"type":"text","text":" to "},{"type":"inlineMath","attrs":{"latex":"(3x - 5)"}},{"type":"text","text":", and $5$ to $(2x + 3)$."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Combine like terms on both sides of the equation."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Move all terms involving "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":" to one side and constants to the other."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Solve for "},{"type":"inlineMath","attrs":{"latex":"x"}},{"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":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"x = 2"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"After distributing and combining like terms, you solve for "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":" and get "},{"type":"inlineMath","attrs":{"latex":"x = 2"}},{"type":"text","text":"."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q22. Solve the rational equation: "},{"type":"inlineMath","attrs":{"latex":"\\frac{1}{3x} + \\frac{2}{x + 1} = \\frac{1}{6x}"}}]},{"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 Rational Equations"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to solve equations with rational expressions by finding a common denominator."}]},{"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":"LCD: Least common denominator for all terms."}]}]}]},{"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 for "},{"type":"inlineMath","attrs":{"latex":"3x"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"x + 1"}},{"type":"text","text":", and "},{"type":"inlineMath","attrs":{"latex":"6x"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Multiply both sides of the equation by the LCD to clear denominators."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Simplify and solve the resulting equation for "},{"type":"inlineMath","attrs":{"latex":"x"}},{"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":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"x = 1"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"After clearing denominators and solving, "},{"type":"inlineMath","attrs":{"latex":"x = 1"}},{"type":"text","text":"."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q23. Write the line "},{"type":"inlineMath","attrs":{"latex":"5x - 3y = 30"}},{"type":"text","marks":[{"type":"bold"}],"text":" in slope-intercept form"}]},{"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-Intercept Form"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to solve for "},{"type":"inlineMath","attrs":{"latex":"y"}},{"type":"text","text":" and write the equation in the form "},{"type":"inlineMath","attrs":{"latex":"y = mx + b"}},{"type":"text","text":"."}]},{"type":"he