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Step-by-Step Guidance for College Algebra Practice Problems

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Q1. Solve the equation:

Background

Topic: Solving Linear Equations

This question tests your ability to solve linear equations by applying the distributive property, combining like terms, and isolating the variable.

Key Terms and Formulas

  • Distributive Property:

  • Combining Like Terms: Add or subtract terms with the same variable.

  • Isolating the Variable: Rearranging the equation to solve for .

Step-by-Step Guidance

  1. Apply the distributive property to to expand the equation.

  2. Combine like terms on the left side of the equation.

  3. Move all terms containing to one side and constants to the other side.

  4. Simplify the equation to isolate .

Try solving on your own before revealing the answer!

Final Answer:

After distributing, combining like terms, and isolating , you find that .

Q2. Perform the indicated operations:

Background

Topic: Complex Numbers (Multiplication)

This question tests your ability to multiply complex numbers using the distributive property (FOIL method) and simplify the result.

Key Terms and Formulas

  • Complex Number: A number in the form , where is the imaginary unit ().

  • FOIL Method: Multiply each term in the first binomial by each term in the second binomial.

Step-by-Step Guidance

  1. Use the distributive property (FOIL) to expand .

  2. Multiply each term: , , , and .

  3. Combine the real and imaginary parts.

  4. Remember that and use this to simplify the expression.

Try solving on your own before revealing the answer!

Final Answer:

After expanding and simplifying, the product is .

Q3. Solve the inequality and write the solution set in interval notation:

Background

Topic: Compound Inequalities

This question tests your ability to solve compound (double) inequalities and express the solution in interval notation.

Key Terms and Formulas

  • Compound Inequality: An inequality with two comparison symbols, representing a range of values.

  • Interval Notation: A way to write the set of solutions using brackets and parentheses.

Step-by-Step Guidance

  1. Subtract $20y$.

  2. Simplify each part after subtraction.

  3. Divide all parts by $2y$.

  4. Write the solution in interval notation.

Try solving on your own before revealing the answer!

Final Answer:

The solution set in interval notation is .

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