7th Grade Equivalent Linear Expressions Test Solutions and Scoring (PDF)

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

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This grade 7 equivalent expressions test 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 and scoring guide to grade the equivalent expressions test. Each solution shows the full work, and the scoring note explains how the points are awarded. Give partial credit for correct steps even when the final answer is wrong.

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

Grade 7 equivalent expressions test answers: worked solutions

Question 1 – Combine like terms [2 pts]

\((9x+2x)+(-4+10)=11x+6\)

\(11x+6\)

Scoring: 1 point for combining the x terms; 1 point for combining the constants.

Question 2 – Area model [2 pts]

\(4(x+5)=4x+20\)

\(4(x+5)=4x+20\)

4(x + 5) = 4x + 20.

Scoring: 1 point for the product; 1 point for the sum.

Question 3 – Distribute [2 pts]

\(-6y+21+5=-6y+26\)

\(-6y+26\)

Scoring: 1 point for distributing correctly; 1 point for combining constants.

Question 4 – Factor [2 pts]

The GCF of 18 and 24 is 6.

\(18x+24=6(3x+4)\)

\(6(3x+4)\)

Scoring: 1 point for the GCF; 1 point for the factored form.

Question 5 – Subtract [2 pts]

\(5x-2-3x+8=2x+6\)

\(2x+6\)

Scoring: 1 point for changing the signs; 1 point for the final expression.

Question 6 – Rational coefficients [2 pts]

\(\frac{4}{6}x-\frac{1}{6}x=\frac{3}{6}x=\frac{1}{2}x\)

\(\frac{1}{2}x\)

Scoring: 1 point for a common denominator; 1 point for the simplified result.

Question 7 – Equivalent? [2 pts]

The values of \(2(x+3)\) and \(2x+6\) are equal in both rows; \(2x+3\) is different.

Expanding confirms \(2(x+3)=2x+6\).

\(2(x+3)\) and \(2x+6\)

2(x+3) and 2x+6 agree.

Scoring: 1 point for the completed table; 1 point for the equivalent pair with a reason.

Question 8 – Rectangle [3 pts]

\(2w+2(w+8)=4w+16\).
\(4(12)+16=64\) units.
\(5(w+8)=5w+40\).

5(w + 8) = 5w + 40.

Scoring: 1 point for each part.

Question 9 – Discount and tax [3 pts]

\(p-0.20p=0.8p\)
\(0.8p\times 1.05=0.84p\)
\(0.84(60)=50.40\) dollars.

Scoring: 1 point for each part.

Total score

Total

20 points

Key facts behind this grade 7 equivalent expressions test 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 test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 7 chapters: Grade 7 math.

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