7th Grade Equivalent Linear Expressions Worksheet Solutions (PDF)

7th Grade math worksheet solutions: Equivalent Linear Expressions – Maths PDF

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This grade 7 equivalent expressions answers for 7th Grade covers equivalent linear expressions (Common Core 7.EE.A.1, 7.EE.A.2), with a free PDF to print.

Use this answer key to check your work on the equivalent expressions worksheet. Every solution shows the steps, and the final answer appears in bold. If your answer is different, compare each step and look for the first place where the work changes.

Grade 7 · Common Core State Standards: 7.EE.A.1, 7.EE.A.2

Grade 7 equivalent expressions answers: exercises 1 to 10

Exercise 1 – Combine like terms

$3+5=8$, so $3x+5x=8x$.

$8x$

Exercise 2 – Terms and constants

$7y-2y=5y$; the constant 4 stays.

$5y+4$

Exercise 3 – Group like terms

$(4a+2a)+(3-7)=6a-4$

$6a-4$

Exercise 4 – Distribute

$3\cdot x+3\cdot 4=3x+12$

$3x+12$

3(x + 4) = 3x + 12.

Exercise 5 – Distribute a negative

$(-2)(y)+(-2)(-5)=-2y+10$

$-2y+10$

Exercise 6 – Factor out the GCF

The GCF of 6 and 12 is 6.

$6x+12=6(x+2)$

$6(x+2)$

6x + 12 = 6(x + 2).

Exercise 7 – Factor with subtraction

The GCF of 15 and 10 is 5.

$15a-10=5(3a-2)$

$5(3a-2)$

Exercise 8 – Subtract expressions

Add the opposite: $7x+3-2x+4$.

$=5x+7$

$5x+7$

Exercise 9 – Add expressions

$3x+2x=5x$ and $-5+9=4$.

$5x+4$

Exercise 10 – Fraction coefficients

$\frac{2}{4}+\frac{3}{4}=\frac{5}{4}$

$\frac{5}{4}x$

Check with x = 4.

Exercises 11 and up

Exercise 11 – Decimal coefficient

$0.4\cdot 5x=2x$ and $0.4\cdot(-10)=-4$.

$2x-4$

Exercise 12 – Expand and combine

$6x+2+4x-8$

$=10x-6$

$10x-6$

Exercise 13 – Factor a fraction

$3=\frac{1}{2}\cdot 6$, so $\frac{1}{2}x+3=\frac{1}{2}(x+6)$.

$\frac{1}{2}(x+6)$

Exercise 14 – Equivalent or not?

At $x=1$: $3(2-4)=-6$ but $6-4=2$.

Expanding gives $3(2x-4)=6x-12$.

No, the expressions are not equivalent

The values differ.

Exercise 15 – Perimeter of a rectangle

$P=2w+2(w+5)=2w+2w+10=4w+10$.

For $w=7$: $4(7)+10=38$.

$4w+10$; 38 feet

Exercise 16 – School store

$2.5n+4$.

$2.5(6)+4=15+4=19$

$2.5n+4$; $19

Exercise 17 – Sales tax form

$p+0.08p=1p+0.08p=1.08p$.

$1.08(25)=27$.

$1.08p$; $27

Exercise 18 – Discount form

$x-0.25x=0.75x$.

$0.75(48)=36$

$0.75x$; $36

Exercise 19 – Triangle perimeter

$(x+3)+(2x-1)+(3x+2)=6x+4$.

$6(5)+4=34$

$6x+4$; 34 inches

Exercise 20 – Garden area

Product: $5(x+3)$. Sum: $5x+15$.

Check: $5(6+3)=45$ and $5(6)+15=45$.

$5(x+3)=5x+15$; 45 square feet

Key facts behind this grade 7 equivalent expressions answers

Key facts

Like terms have the same variable part and can be combined by adding coefficients.
Distributive property: $a(b + c) = ab + ac$.
Factor by pulling out the greatest common factor: $6x + 12 = 6(x + 2)$.
Subtracting an expression means adding its opposite.
Adding $5\%$ tax to a price p gives $p + 0.05p = 1.05p$.

How to use this grade 7 equivalent expressions answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

All Grade 7 chapters: Grade 7 math.

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