Sure! Here’s a sample set of questions that might be found in a unit test for a lesson on variable equations and inequalities. You can use these as practice problems:
Variable Equations and Inequalities Unit Test
Name: _______________________ Date: ___________
Part 1: Solve the equations.
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\( 3x + 5 = 20 \)
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\( 4(y - 3) = 16 \)
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\( 7 - 2z = 3 + 5z \)
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\( \frac{1}{2}x - 6 = 10 \)
Part 2: Solve the inequalities and represent the solution on a number line.
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\( 5x - 9 < 16 \)
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\( -3(y + 2) \geq 12 \)
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\( \frac{x}{4} + 2 \leq 3 \)
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\( 2m + 5 > 3m - 1 \)
Part 3: Word Problems
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A number is increased by 7 and the result is less than 20. Write an inequality for the situation and solve for the number.
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The sum of three times a number and 4 is greater than or equal to 19. Write an equation and solve for the number.
Part 4: Multiple Choice
- What is the solution set for the inequality \( x - 3 > 5 \)?
a) \( x > 2 \)
b) \( x < 8 \)
c) \( x > 8 \)
d) \( x < 2 \)
- Solve for \( x \) in the equation \( 2(x + 4) = 16 \).
a) \( x = 4 \)
b) \( x = 8 \)
c) \( x = -4 \)
d) \( x = -8 \)
Answer Key (For Teacher Use)
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\( x = 5 \)
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\( y = 7 \)
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\( z = \frac{2}{9} \)
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\( x = 32 \)
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\( x < 5 \)
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\( y \leq -6 \)
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\( x \leq 4 \)
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\( m < 6 \)
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\( x + 7 < 20 \) → \( x < 13 \)
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\( 3x + 4 \geq 19 \) → \( 3x \geq 15 \) → \( x \geq 5 \)
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c) \( x > 8 \)
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a) \( x = 4 \)
Feel free to modify any of the questions or the answer key as needed based on your particular curriculum!