One and two step equations unit test

1 answer

Sure! Here's a brief unit test for one-step and two-step equations, covering key concepts:

One and Two-Step Equations Unit Test

Name: ____________________ Date: ___________


Part A: One-Step Equations

Solve for \( x \) in the following equations:

  1. \( x + 5 = 12 \)

  2. \( 7x = 42 \)

  3. \( x - 9 = 4 \)

  4. \( \frac{x}{4} = 3 \)

  5. \( -2 = x + 3 \)


Part B: Two-Step Equations

Solve for \( x \) in the following equations:

  1. \( 2x + 3 = 11 \)

  2. \( 5x - 7 = 18 \)

  3. \( \frac{x}{3} + 4 = 10 \)

  4. \( 3(x - 2) = 12 \)

  5. \( -4x + 8 = 0 \)


Part C: Word Problems

  1. A number decreased by 7 equals 15. What is the number?

  2. Four times a number is equal to 28. What is the number?

  3. If you add 12 to a number and then divide by 3, you get 8. What is the number?


Instructions:

  • Show all steps in your calculations.
  • Simplify your answers.
  • Make sure to double-check your work.

Answer Key

Part A: One-Step Equations

  1. \( x + 5 = 12 \) ➔ \( x = 12 - 5 \) ➔ \( x = 7 \)

  2. \( 7x = 42 \) ➔ \( x = 42 / 7 \) ➔ \( x = 6 \)

  3. \( x - 9 = 4 \) ➔ \( x = 4 + 9 \) ➔ \( x = 13 \)

  4. \( \frac{x}{4} = 3 \) ➔ \( x = 3 * 4 \) ➔ \( x = 12 \)

  5. \( -2 = x + 3 \) ➔ \( x = -2 - 3 \) ➔ \( x = -5 \)

Part B: Two-Step Equations

  1. \( 2x + 3 = 11 \) ➔ \( 2x = 11 - 3 \) ➔ \( 2x = 8 \) ➔ \( x = 4 \)

  2. \( 5x - 7 = 18 \) ➔ \( 5x = 18 + 7 \) ➔ \( 5x = 25 \) ➔ \( x = 5 \)

  3. \( \frac{x}{3} + 4 = 10 \) ➔ \( \frac{x}{3} = 10 - 4 \) ➔ \( \frac{x}{3} = 6 \) ➔ \( x = 18 \)

  4. \( 3(x - 2) = 12 \) ➔ \( x - 2 = 12 / 3 \) ➔ \( x - 2 = 4 \) ➔ \( x = 6 \)

  5. \( -4x + 8 = 0 \) ➔ \( -4x = -8 \) ➔ \( x = 2 \)

Part C: Word Problems

  1. Let the number be \( x \):
    \( x - 7 = 15 \) ➔ \( x = 15 + 7 \) ➔ \( x = 22 \)

  2. Let the number be \( x \):
    \( 4x = 28 \) ➔ \( x = 28 / 4 \) ➔ \( x = 7 \)

  3. Let the number be \( x \):
    \( \frac{x + 12}{3} = 8 \) ➔ \( x + 12 = 24 \) ➔ \( x = 24 - 12 \) ➔ \( x = 12 \)


Feel free to adjust the questions or format as needed!