8th Grade Solving Linear Equations in One Variable Test Solutions and Scoring (PDF)

8th Grade math test solutions: Solving Linear Equations in One Variable – Maths PDF

Cover of the book Grade 8 Math Tests with Answer Keys (PDF)

Download as a PDFThe Grade 8 tests book with answer keysPrintable PDFSee the book ›

Sommaire

This grade 8 linear equations test answers for 8th Grade covers solving linear equations in one variable (Common Core 8.EE.C.7a, 8.EE.C.7b), with a free PDF to print.

Use this answer key to score the linear equations test out of 20 points. Each solution shows the full work and a scoring guide, so partial credit can be given fairly when a student shows correct steps but makes an arithmetic slip.

Grade 8 · Common Core State Standards: 8.EE.C.7a, 8.EE.C.7b

Grade 8 linear equations test answers: worked solutions

Question 1 – Solve [3 pts]

\(4x = 24\), so \(x = 6\).
\(4x = 16\), so \(x = 4\).

Scoring: Part a: 1 point. Part b: 1 point for collecting terms, 1 point for the answer.

Question 2 – Distribute [3 pts]

\(5x – 10 = 3x + 8\). Then \(2x = 18\), so \(x = 9\).

Scoring: 1 point for distributing. 1 point for collecting terms. 1 point for \(x = 9\).

Question 3 – Fractions [2 pts]

Multiply by 6: \(2x + 12 = x + 30\), so \(x = 18\).

Scoring: 1 point for clearing fractions. 1 point for \(x = 18\).

Question 4 – Number of solutions [3 pts]

Infinitely many: \(3x + 6 = 3x + 6\).
No solution.
Subtracting \(2x\) gives \(7 = -1\), a false statement.

Scoring: 1 point per part.

Question 5 – Triangle [3 pts]

Angles of a triangle add to 180 degrees.

\(x + (x + 20) + 2x = 180\), so \(4x = 160\) and \(x = 40\).

Angles: 40°, 60°, 80°.

Scoring: 1 point for the equation, 1 point for \(x = 40\), 1 point for the three angles.

Question 6 – Rectangle [2 pts]

x = 5.

\(2(2x + 1) + 2(x + 3) = 38\), so \(6x + 8 = 38\) and \(x = 5\).

Scoring: 1 point for the equation. 1 point for \(x = 5\).

Question 7 – Compare plans [3 pts]

\(10x + 15 = 15x\), so \(15 = 5x\) and \(x = 3\).

Scoring: 1 point for the equation. 1 point for solving. 1 point for 3 weeks.

Question 8 – Explain [1 pt]

It is true for every value of \(x\), since the variable disappeared.

Scoring: 1 point for a correct explanation.

Total score

Total

20 points

Key facts behind this grade 8 linear equations test answers

Key facts

Do the same thing to both sides to keep the equation balanced.
Distribute first, then combine like terms, then collect variable terms.
One solution: \(x = \text{number}\). No solution: false statement. Infinitely many: true statement.
Multiply by a common multiple to clear fractions and decimals.
Always check by substituting your answer into the original equation.

How to use this grade 8 linear equations 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 8 chapters: Grade 8 math.

Voter.. post

Free printable PDF