This grade 8 linear test answer key gives the full solution and the scoring guide for each of the 8 test questions on solving linear equations.
Use this key to score the test out of 20 points. Each solution shows the full work, and the scoring note explains how partial credit is awarded. Accept any correct method, such as clearing fractions first or working with the fractions directly.
Grade 8 Linear Test Answer Key: questions 1–5
Question 1: Multi-step equations (2 points)
- \(5x=25\), so \(x=5\).
- \(3x-12=-21\), so \(3x=-9\) and \(x=-3\).
Scoring: 1 point per part. Accept a correct answer with minor arithmetic work not shown.
Question 2: Variables on both sides (3 points)
- \(4x+5=25\), so \(4x=20\) and \(x=5\).
- \(4x-8=x+10\), so \(3x=18\) and \(x=6\).
- \(6x+3-4x=19\), so \(2x+3=19\), \(2x=16\) and \(x=8\).
Scoring: 1 point per part.
Question 3: Fractions and decimals (3 points)
- \(\frac{2}{5}x=8\), so \(x=8\times \frac{5}{2}=\)20.
- \(0.5x-0.5=2\), so \(0.5x=2.5\) and \(x=5\).
- Multiply by 6: \(2(x+6)=3x-6\), so \(2x+12=3x-6\) and \(x=18\). Check: \(\frac{1}{3}(24)=8\) and \(\frac{1}{2}(18)-1=8\).
Scoring: 1 point per part.
Question 4: Number of solutions (3 points)
- \(7x-2=7x-2\) is always true: infinitely many solutions.
- \(3x+12=3x+9\) gives \(12=9\), false: no solution.
- \(6x-4=2x+4\), so \(4x=8\): one solution, \(x=2\).
Scoring: 1 point per part: 1 for the correct classification with supporting work, solving for part (c).
Question 5: Choose the constant (2 points)
- \(3(x+2)=3x+6\), so the sides match only when \(k=6\).
- Any value other than 6 works, for example \(k=10\): \(3x+6=3x+10\) gives \(6=10\), which is false.
Scoring: 1 point per part. Accept any k other than 6 in part (b).
Grade 8 Linear Test Answer Key: questions 6–8
Question 6: Equal perimeters (2 points)
Rectangle: \(2(2x+1+5)=4x+12\). Square: \(4(x+7)=4x+28\).
Equation: \(4x+12=4x+28\). Subtract \(4x\): \(12=28\), which is false.
No solution. The square’s perimeter is always 16 more, so the perimeters are never equal.
Scoring: 1 point for a correct equation; 1 point for no solution with a reason.
Question 7: Savings plans (3 points)
- Priya: \(64+8w\). Sam: \(28+14w\).
- \(64+8w=28+14w\), so \(36=6w\) and \(w=6\). After 6 weeks.
- \(64+8(6)=112\). Each has $112.
Scoring: 1 point per part.
Question 8: Find the error (2 points)
Noah did not multiply \(-2\) by 4 when he distributed. Correct: \(4(x-2)=4x-8\).
Then \(4x-8=2x+6\), so \(2x=14\) and \(x=7\). Check: \(4(5)=20\) and \(2(7)+6=20\).
Scoring: 1 point for identifying the distribution error; 1 point for the correct solution x = 7.
Scoring summary
20 points: add the points of every question of this grade 8 linear test answer key.
How to use this grade 8 linear test answer key
Use this grade 8 linear test answer key to score the test fairly and to see which skills need more practice.
See every chapter on the Grade 8 math page.
