Equivalent Expressions Worksheet Answer Key – Grade 7

Problem 1 Combine Three Like Terms

The terms are all like terms, so combine the coefficients: 9 + 4 − 3 = 10.

10y

Problem 2 Expand a Sum

6 · x = 6x and 6 · 7 = 42.

6x + 42

Problem 3 Expand a Difference

5 · 2a = 10a and 5 · 3 = 15, keeping the minus sign.

10a − 15

Problem 4 Test for Equivalence

The first row gives 14, 21, 28, 35 and the second row gives 2, 9, 16, 23. The values differ in every column, so Jaylen is wrong. The correct expansion is 7x + 14.

Not equivalent

Problem 5 Expand with a Negative Factor

−3 · 4x = −12x and −3 · (−5) = +15.

−12x + 15

Problem 6 Combine Terms in Four Pieces

x terms: 8 + 2 − 5 = 5. Constants: −3 + 11 = 8.

5x + 8

Problem 7 Expand with a Fraction

34 · 8x = 6x and 34 · 12 = 9.

6x − 9

Problem 8 Expand with a Decimal

−0.5 · 6x = −3x and −0.5 · 9.2 = −4.6.

−3x − 4.6

Problem 9 Factor from an Area Model

The GCF of 18 and 24 is 6, which becomes the height. The widths are 18x ÷ 6 = 3x and 24 ÷ 6 = 4.

6(3x + 4)

Problem 10 Factor with a Negative GCF

Factor out −4: −8x ÷ (−4) = 2x and −20 ÷ (−4) = 5. Check: −4 · 2x = −8x and −4 · 5 = −20.

−4(2x + 5)

Problem 11 Subtract an Expression

Subtracting flips both signs: 3x + 2 − 5x + 7. Then 3x − 5x = −2x and 2 + 7 = 9.

−2x + 9

Problem 12 Add Fractional Coefficients

x terms: 23 + 13 = 1. Constants: 14 − 34 = −12.

x − 12

Problem 13 Two Distributions Then Combine

First part: 8x − 12. Second part: 6x + 9. Combine: 8x + 6x = 14x and −12 + 9 = −3.

14x − 3

Problem 14 Factor a Decimal Expression

1.5x ÷ 1.5 = x and 4.5 ÷ 1.5 = 3. Check: 1.5 · x = 1.5x and 1.5 · 3 = 4.5.

1.5(x − 3)

Problem 15 Perimeter of a Garden

Fencing = 2(5x + 1) + 2(2x + 4) = 10x + 2 + 4x + 8 = 14x + 10.

For x = 2: sides 11 ft and 8 ft, so 2(11 + 8) = 38, and 14(2) + 10 = 38.

14x + 10 feet; 38 feet when x = 2

Problem 16 Price with Sales Tax

Total = p + 0.08p = 1.08p. For p = 45: 1.08 × 45 = 48.60.

1.08p; $48.60

Problem 17 Clearance Discount

Sale price = p − 0.35p = 0.65p. For p = 80: 0.65 × 80 = 52.

0.65p; $52

Problem 18 Fundraiser Revenue

Revenue = 15x + 25(x − 4) = 15x + 25x − 100 = 40x − 100.

For x = 18: shirts 270 and hats 25 · 14 = 350, total 620. Also 40(18) − 100 = 620.

40x − 100 dollars; $620 when x = 18

Problem 19 Find the Error

Expand: 6x − 12 − 2x + 10 = 4x − 2, so Ines is correct.

Check x = 3: original 3(2) − 2(−2) = 6 + 4 = 10; Ines: 4(3) − 2 = 10; Cal: 12 − 22 = −10.

Cal treated −2 · (−5) as −10 instead of +10.

Ines is correct: 4x − 2

Problem 20 Three Trail Sections

Section 2 = 34(2x + 1.5) = 1.5x + 1.125. Section 3 = (2x + 1.5) − (x − 0.25) = x + 1.75.

Total: 2x + 1.5 + 1.5x + 1.125 + x + 1.75 = 4.5x + 4.375.

For x = 2: sections are 5.5, 4.125 and 3.75 miles, total 13.375.

4.5x + 4.375 miles; 13.375 miles when x = 2