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:
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\( x + 5 = 12 \)
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\( 7x = 42 \)
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\( x - 9 = 4 \)
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\( \frac{x}{4} = 3 \)
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\( -2 = x + 3 \)
Part B: Two-Step Equations
Solve for \( x \) in the following equations:
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\( 2x + 3 = 11 \)
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\( 5x - 7 = 18 \)
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\( \frac{x}{3} + 4 = 10 \)
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\( 3(x - 2) = 12 \)
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\( -4x + 8 = 0 \)
Part C: Word Problems
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A number decreased by 7 equals 15. What is the number?
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Four times a number is equal to 28. What is the number?
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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
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\( x + 5 = 12 \) ➔ \( x = 12 - 5 \) ➔ \( x = 7 \)
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\( 7x = 42 \) ➔ \( x = 42 / 7 \) ➔ \( x = 6 \)
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\( x - 9 = 4 \) ➔ \( x = 4 + 9 \) ➔ \( x = 13 \)
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\( \frac{x}{4} = 3 \) ➔ \( x = 3 * 4 \) ➔ \( x = 12 \)
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\( -2 = x + 3 \) ➔ \( x = -2 - 3 \) ➔ \( x = -5 \)
Part B: Two-Step Equations
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\( 2x + 3 = 11 \) ➔ \( 2x = 11 - 3 \) ➔ \( 2x = 8 \) ➔ \( x = 4 \)
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\( 5x - 7 = 18 \) ➔ \( 5x = 18 + 7 \) ➔ \( 5x = 25 \) ➔ \( x = 5 \)
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\( \frac{x}{3} + 4 = 10 \) ➔ \( \frac{x}{3} = 10 - 4 \) ➔ \( \frac{x}{3} = 6 \) ➔ \( x = 18 \)
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\( 3(x - 2) = 12 \) ➔ \( x - 2 = 12 / 3 \) ➔ \( x - 2 = 4 \) ➔ \( x = 6 \)
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\( -4x + 8 = 0 \) ➔ \( -4x = -8 \) ➔ \( x = 2 \)
Part C: Word Problems
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Let the number be \( x \):
\( x - 7 = 15 \) ➔ \( x = 15 + 7 \) ➔ \( x = 22 \) -
Let the number be \( x \):
\( 4x = 28 \) ➔ \( x = 28 / 4 \) ➔ \( x = 7 \) -
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!