Equivalent Expressions Test Answer Key with Scoring – Grade 7

Question 1 Expand Two Expressions (2 points)

1. 7 · 3x − 7 · 4 = 21x − 28.
2. −2.5 · 4x = −10x and −2.5 · 6 = −15, so −10x − 15.

Scoring: 1 point per part.

Question 2 Combine Like Terms (2 points)

x terms: 5 − 3 + 2 = 4. Constants: −8 + 14 = 6.

4x + 6

Scoring: 1 point for each correctly combined group.

Question 3 Factor Out the GCF (2 points)

1. GCF of 28 and 42 is 14: 14(2x + 3).
2. GCF is 3, and factoring out −3 gives −3(3x + 5). Accept 3(−3x − 5).

Scoring: 1 point per part; award it only if the factoring is complete.

Question 4 Simplify and Verify (3 points)

1. 2(5x − 3) = 10x − 6 and −4(x − 2.5) = −4x + 10. Combine: 6x + 4.
2. At x = 3: 2(12) − 4(0.5) = 24 − 2 = 22, and 6(3) + 4 = 22. Both equal 22.

Scoring: part a, 1 point for each correct distribution; part b, 1 point.

Question 5 Rectangle Perimeter (3 points)

1. P = 2(2x + 7) + 2(x − 3) = 4x + 14 + 2x − 6 = 6x + 8 cm.
2. For x = 6: 6(6) + 8 = 44 cm. Check: sides 19 and 3, so 2(19 + 3) = 44.

Scoring: part a, 1 point for setting up the sum and 1 point for the simplified result; part b, 1 point.

Question 6 Fraction Coefficients (2 points)

34(12x − 8) = 9x − 6 and 12(6x + 10) = 3x + 5. Sum: 12x − 1.

12x − 1

Scoring: 1 point for both distributions, 1 point for the sum.

Question 7 Price Increase (3 points)

1. p + 0.12p = 1.12p.
2. 1.12 × 75 = 84, so $84.
3. 1.12 means the new price is 112% of the old price: the original 100% plus a 12% increase.

Scoring: 1 point per part.

Question 8 Error Analysis (3 points)

1. The student multiplied −3 by −7 and got −21; a negative times a negative is positive.
2. −3(2x − 7) = −6x + 21, so −6x + 21.
3. At x = 2: original −3(4 − 7) = 9; student −12 − 21 = −33; correct −12 + 21 = 9. Since −33 ≠ 9, the student’s answer is not equivalent.

Scoring: 1 point per part.