8th Grade Solving Linear Equations in One Variable Worksheet Solutions (PDF)

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

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This grade 8 linear equations 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.

This answer key gives a full worked solution for each of the 20 problems on the linear equations worksheet (Common Core 8.EE.C.7a and 8.EE.C.7b). Compare each step with your own work, not only the final answer, and note any step where your method differed.

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

Grade 8 linear equations answers: exercises 1 to 10

Exercise 1 – Two-step equation

Subtract 5: $3x = 15$.

Divide by 3: $x = 5$.

$x = 5$

Exercise 2 – Fractional coefficient

Add 4: $\frac{2}{3}x = 12$.

Multiply by $\frac{3}{2}$: $x = 18$.

$x = 18$

Exercise 3 – Combine like terms

Combine: $5x – 4 = 21$, so $5x = 25$.

$x = 5$

Exercise 4 – Variables on both sides

Subtract $2x$: $3x – 7 = 11$.

Add 7: $3x = 18$, so $x = 6$.

$x = 6$

Exercise 5 – Distribute

$6x + 6 = 4x + 20$, so $2x = 14$.

$x = 7$

Exercise 6 – Distribute on both sides

$6x + 3 = 5x + 10$.

Subtract $5x$: $x + 3 = 10$, so $x = 7$.

$x = 7$

Exercise 7 – No solution

$6x + 2 = 6x + 12$. Subtract $6x$: $2 = 12$, which is false.

No solution

Exercise 8 – Infinitely many

$3x + 12 = 3x + 12$. Subtract $3x$: $12 = 12$, which is always true.

Infinitely many solutions

Exercise 9 – Fractions on both sides

Multiply every term by 6: $4x – 6 = x + 24$.

Then $3x = 30$.

$x = 10$

Exercise 10 – Decimals

Multiply by 4: $2x + 10 = x + 16$.

$x = 6$.

$x = 6$

Exercises 11 and up

Exercise 11 – Negative sign distribution

$7 – 2x + 2 = 3x – 6$, so $9 – 2x = 3x – 6$.

Add $2x$ and 6: $15 = 5x$.

$x = 3$

Exercise 12 – Classify

$1 = -3$ is false: no solution.
$4x + 2 = 4x + 2$ is true: infinitely many.
$x = 5$: one solution.

Exercise 13 – Find the constant

The variable terms match, so the equation is $7 = c$.

Infinitely many if $c = 7$; no solution if $c \neq 7$

Exercise 14 – Number puzzle

$3x – 4 = x + 10$, so $2x = 14$.

Exercise 15 – Rectangle perimeter

Length 13 ft, width 7 ft.

$2(x + 5) + 2(x – 1) = 40$, so $4x + 8 = 40$ and $x = 8$.

$x = 8$; 13 ft by 7 ft

Exercise 16 – Gym plans

The lines cross at 4 months.

$12x + 20 = 17x$, so $20 = 5x$ and $x = 4$.

Cost: $17 \cdot 4 = 68$.

4 months, at \$68 each

Exercise 17 – Saving up

$45 + 8x = 15 + 13x$, so $30 = 5x$ and $x = 6$.

Amount: $45 + 8 \cdot 6 = 93$.

After 6 weeks, \$93 each

Exercise 18 – Triangle angles

Angles 30, 70 and 80 degrees.

$x + (2x + 10) + (3x – 10) = 180$, so $6x = 180$ and $x = 30$.

30°, 70° and 80°

Exercise 19 – Phone plan

$25 + 0.10x = 40$, so $0.10x = 15$.

150 minutes

Exercise 20 – Explain no solution

No. Subtracting $2x$ from both sides gives a false statement, which means no value of $x$ works. The equation has no solution.

Liam made no error

Key facts behind this grade 8 linear equations 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 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 8 chapters: Grade 8 math.

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