Testinar Grade 8 math

Solving Linear Equations in One Variable

Learn to reason about and solve Grade 8 problems involving Solving Linear Equations in One Variable.

CH03-04 Equations, Inequalities, and Systems
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. Look at the table of values for the equation \(y=2x+1\): What value of \(x\) produces \(y=9\)?

    Solving Linear Equations in One Variable visual for G8-C03-T04-Q032
    1. \(x=3\)
    2. \(x=5\)
    3. \(x=8\)
    4. \(x=4\)

  2. Solve for \(x\): \(3(x-4)=2x+5\)

    1. \(x=-7\)
    2. \(x=7\)
    3. \(x=17\)
    4. \(x=9\)

  3. Solve for \(x\): \(2x+8=20\)

    1. \(x=6\)
    2. \(x=14\)
    3. \(x=28\)
    4. \(x=4\)

  4. Solve for \(x\): \(5x-3=2x+9\)

    1. \(x=2\)
    2. \(x=12\)
    3. \(x=6\)
    4. \(x=4\)

  5. Solve for \(y\): \(-4y+7=15\)

    1. \(y=-8\)
    2. \(y=8\)
    3. \(y=2\)
    4. \(y=-2\)

  6. What is the solution to \(6(x+2)=30\)?

    1. \(x=3\)
    2. \(x=5\)
    3. \(x=8\)
    4. \(x=-2\)

  7. Solve for \(x\): \(\frac{x}{3}+5=9\)

    1. \(x=12\)
    2. \(x=36\)
    3. \(x=8\)
    4. \(x=14\)

  8. Two students solve \(2x+5=11\) and get different answers: Student A gets \(x=3\) and Student B gets \(x=4\). Without solving, how can you determine which student is correct?

    1. Substitute each value into the original equation to check which one works
    2. Solve the equation and see who matched your answer
    3. Check which value is smaller
    4. Divide 11 by 2 to see which is closer
Teacher and parent reference

Answer key and explanations

  1. D. \(x=4\)

    Use \(y=2x+1\): \(9=2x+1 \Rightarrow 8=2x \Rightarrow x=4\).

  2. C. \(x=17\)

    Distribute: \(3x-12=2x+5\). Subtract \(2x\): \(x-12=5\). Add \(12\): \(x=17\). Check: \(3(17-4)=3(13)=39\) and \(2(17)+5=39\) ✓. (Distractor B from forgetting to distribute the 3; D from arithmetic error.)

  3. A. \(x=6\)

    Subtract \(8\) from both sides: \(2x=12\). Divide by \(2\): \(x=6\). Check: \(2(6)+8=12+8=20\) ✓.

  4. D. \(x=4\)

    Subtract \(2x\) and add \(3\): \(3x=12\). Divide by \(3\): \(x=4\). (Distractor A: result of dividing 12 by \(3\) incorrectly; C: forgetting to distribute constant; D: result of incorrect arithmetic.)

  5. D. \(y=-2\)

    Subtract \(7\): \(-4y=8\). Divide by \(-4\): \(y=-2\).

  6. A. \(x=3\)

    Distribute: \(6x+12=30\). Subtract \(12\): \(6x=18\). Divide by \(6\): \(x=3\).

  7. A. \(x=12\)

    Subtract \(5\): \(\frac{x}{3}=4\). Multiply by \(3\): \(x=12\).

  8. A. Substitute each value into the original equation to check which one works

    Substitution is the definitive test: \(2(3)+5=11\) ✓ and \(2(4)+5=13 \neq 11\) ✗. Student A is correct.

Free Testinar sample Reviewed November 6, 2026 testinar.com
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