Question

One and two step equations unit test

Answer 1

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: ___________**

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

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**Part B: Two-Step Equations**

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

6. \( 2x + 3 = 11 \)

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

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

9. \( 3(x - 2) = 12 \)

10. \( -4x + 8 = 0 \)

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**Part C: Word Problems**

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

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

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

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

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### 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**

6. \( 2x + 3 = 11 \) ➔ \( 2x = 11 - 3 \) ➔ \( 2x = 8 \) ➔ \( x = 4 \)

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

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

9. \( 3(x - 2) = 12 \) ➔ \( x - 2 = 12 / 3 \) ➔ \( x - 2 = 4 \) ➔ \( x = 6 \)

10. \( -4x + 8 = 0 \) ➔ \( -4x = -8 \) ➔ \( x = 2 \)

**Part C: Word Problems**

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

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

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

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Feel free to adjust the questions or format as needed!