Grade 8 Linear Equations Worksheet Answer Key

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Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

Grade 8 Math Worksheet Answer Keys – Mathbot, the Math Made Easy robot coach, with free printable worksheet answer keys for Grade 8

Looking for a linear equations worksheet answer key? Then this answer key gives every step of the Grade 8 worksheet on Solving Multi-Step Linear Equations. Each solution lists the balance steps in order and checks the answer in the original equation where useful. Final answers are in bold; equations with no solution or infinitely many solutions are labeled in words.

Standards: 8.EE.C.7a, 8.EE.C.7b · Level: Grade 8

Problem 1 One-variable equations

(a) Add 8: 5x = 35. Divide by 5: x = 7. (b) Subtract 3: x4 = 6. Multiply by 4: x = 24.

(a) x = 7 (b) x = 24

Problem 2 Variable on both sides

Subtract 2x from both sides: x + 7 = 15. Subtract 7: x = 8. Check: 31 = 31.

x = 8

Problem 3 Distribute first

Distribute: 4x + 12 = 32. Subtract 12: 4x = 20. Divide by 4: x = 5.

x = 5

Problem 4 Combine like terms

Combine: 4x + 9 = 25. Subtract 9: 4x = 16. Divide: x = 4.

x = 4

Problem 5 Fraction coefficient

Multiply both sides by the reciprocal 32: x = 18 · 32 = 27.

x = 27

Problem 6 Balance scale

The equation is 3x + 4 = x + 10. Remove one x from each side: 2x + 4 = 10. Remove 4: 2x = 6. So x = 3.

After removing one x from each side.

x = 3

Problem 7 Both sides variable

(a) Subtract 3x: 4x − 5 = 19. Add 5: 4x = 24. So x = 6. (b) Add 2x: 9 = 7x − 12. Add 12: 21 = 7x. So x = 3.

(a) x = 6 (b) x = 3

Problem 8 Distribute on both sides

Distribute: 6x − 15 = 2x + 14. Subtract 2x: 4x − 15 = 14. Add 15: 4x = 29. So x = 294 = 7.25.

x = 294

Problem 9 Clear the fractions

Multiply every term by 10: 5x + 2x = 140. Then 7x = 140, so x = 20. Check: 10 + 4 = 14.

x = 20

Problem 10 Decimal coefficients

Subtract 0.5x: 3.2 = 0.8x − 0.8. Add 0.8: 4 = 0.8x. Divide by 0.8: x = 5. Check: 5.7 = 5.7.

x = 5

Problem 11 How many solutions?

(a) Subtract 4x: 6 = 9, false, so none (panel A). (b) Distribute: 3x + 6 = 3x + 6, always true, so infinitely many (panel B). (c) 3x = 9, so x = 3 (panel C).

(a) none (b) infinitely many (c) one solution, x = 3

Problem 12 Choosing k

(a) With k = 6 the x terms cancel and leave 5 = −3, which is false. (b) With k = 4 both sides are identical.

(a) k = 6 (b) k = 4

Problem 13 Rational coefficient

Multiply both sides by 87: x + 4 = 16. Subtract 4: x = 12. Check: 78 · 16 = 14.

x = 12

Problem 14 Graph and equation

The lines meet at (3, 7), so x = 3. Algebra: subtract x: 2x − 2 = 4. Add 2: 2x = 6. So x = 3.

Intersection at (3, 7).

x = 3

Problem 15 Gym membership

Set 25 + 18m = 23m. Subtract 18m: 25 = 5m, so m = 5. Cost: 25 + 18 · 5 = 115 and 23 · 5 = 115.

5 months; $115

Problem 16 Two taxi companies

Set 4 + 2.5m = 1.6 + 3.1m. Subtract 2.5m: 4 = 1.6 + 0.6m. Subtract 1.6: 2.4 = 0.6m, so m = 4. Charge: 4 + 2.5 · 4 = 14 and 1.6 + 3.1 · 4 = 14.

4 miles; $14.00

Problem 17 Garden rectangle

Perimeter: 2[(3x + 2) + (x + 5)] = 62. Simplify: 2(4x + 7) = 62, so 4x + 7 = 31 and x = 6. Length = 3 · 6 + 2 = 20 and width = 6 + 5 = 11. Check: 2(31) = 62.

Dimensions.

x = 6; length 20 ft; width 11 ft

Problem 18 Consecutive odd integers

Let the integers be n, n + 2 and n + 4. Then 3n + 6 = 87, so 3n = 81 and n = 27. The integers are 27, 29 and 31, and 27 + 29 + 31 = 87.

27, 29 and 31

Problem 19 What does 8 = 8 mean?

After distributing, both sides are the same expression, 2x + 8. The variable canceled and the statement 8 = 8 is true, so every value of x works. For no solution, try 2x + 3 = 2x + 7, which reduces to the false statement 3 = 7.

Infinitely many solutions; example with none: 2x + 3 = 2x + 7

Problem 20 Fractions on both sides

Multiply every term by 4: (3x − 2) + 4 = 2(x + 7). Simplify: 3x + 2 = 2x + 14. Subtract 2x: x + 2 = 14. So x = 12. Check: 344 + 1 = 9.5 and 192 = 9.5.