Grade 7 Math Practice Test: Two-Step Equations and Inequalities
- Two-Step Equations and Inequalities
- 10 questions
- 15 minutes
This test covers equations of the form px + q = r and p(x + q) = r, two-step inequalities and word problems that lead to them. Tip: when you multiply or divide both sides of an inequality by a negative number, flip the inequality sign.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
Solve: 4x − 7 = 21
Correct answer: A
Add 7 to both sides: 4x = 28. Divide by 4: x = 7. x = 3.5 comes from subtracting 7 instead of adding it.
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Question 2
Solve: x3 + 5 = −4
Correct answer: A
Subtract 5: x3 = −9. Multiply by 3: x = −27. x = −3 divides −9 by 3 instead of multiplying.
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Question 3
Solve: −2(x + 3) = 10
Correct answer: C
Divide both sides by −2: x + 3 = −5, so x = −8. x = 2 ignores the negative sign on the 2.
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Question 4
Liam has $45 saved and adds $12 each week. After how many weeks will he have $153?
Correct answer: D
45 + 12w = 153, so 12w = 108 and w = 9. 12.75 ignores the $45 he already has.
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Question 5
Solve: −3x + 4 > 19
Correct answer: C
Subtract 4: −3x > 15. Dividing by −3 flips the sign: x < −5. x > −5 forgets to flip the inequality.
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Question 6
A phone plan costs $20 per month plus $0.10 per text message. Kim wants her monthly bill to be at most $35. What is the greatest number of texts she can send?
Correct answer: D
20 + 0.10t ≤ 35, so 0.10t ≤ 15 and t ≤ 150. 350 divides $35 by $0.10 and forgets the $20 monthly charge.
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Question 7
Solve: 0.6x + 1.5 = 4.2
Correct answer: B
Subtract 1.5: 0.6x = 2.7. Divide by 0.6: x = 4.5. Check: 0.6 · 4.5 + 1.5 = 2.7 + 1.5 = 4.2.
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Question 8
Solve: 25x − 3 = 7
Correct answer: D
Add 3: 25x = 10. Multiply by 52: x = 25. x = 4 multiplies 10 by 25 instead of dividing by it.
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Question 9
Which value of x is a solution of 5x − 2 ≤ 18?
Correct answer: B
5x ≤ 20, so x ≤ 4. Only 4 fits: 5 · 4 − 2 = 18, which is equal to 18. For 4.5 the left side is 20.5, which is more than 18.
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Question 10
A rectangle is 8 cm wide and has a perimeter of 50 cm. How long is it?
Correct answer: B
2L + 2 · 8 = 50, so 2L = 34 and L = 17 cm. 34 cm is the sum of both lengths, not one length.
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