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Free · Class 6–8 · 6 worksheets · answer keys · practise online · set 7

Linear equations worksheets — simple equations, Class 6 to 8

Free linear equations in one variable worksheets: one-step and two-step simple equations (Class 6–7), variables on both sides and brackets (Class 8), and word problems — with answers.

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One-step equations (+ and −) (Class 6)One-step equations (× and ÷) (Class 6–7)Two-step equations (Class 7)Equations with brackets (Class 7–8)Variables on both sides (Class 8)Equation word problems (Class 7–8)

One-step equations (+ and −)

Class 6 · Worksheet 1 · set 7
Name:Date:Score:    / 12

Solve.

  1. 30 + p = 32
  2. m − 5 = 11
  3. n − 10 = 17
  4. p + 17 = 26
  5. x + 5 = 33
  6. y + 18 = 26
  7. n − 22 = 1
  8. 7 + p = 31
  9. 10 + n = 18
  10. m − 20 = 9
  11. m + 24 = 42
  12. p + 21 = 46

One-step equations (× and ÷)

Class 6–7 · Worksheet 2 · set 7
Name:Date:Score:    / 12

Solve.

  1. m/2 = 7
  2. 6n = 78
  3. 4m = 52
  4. y/8 = 12
  5. y/2 = 9
  6. 9n = 18
  7. m/8 = 15
  8. 6n = 36
  9. 9y = 45
  10. y/2 = 11
  11. p/2 = 12
  12. 7p = 91

Two-step equations

Class 7 · Worksheet 3 · set 7
Name:Date:Score:    / 12

Solve.

  1. 4m + 4 = 24
  2. 7x + 9 = 72
  3. 9y − 16 = 29
  4. 3p − 2 = 22
  5. 2y + 16 = 40
  6. 4p − 15 = 1
  7. 9n − 8 = 10
  8. 6m − 13 = 11
  9. 8m + 9 = 25
  10. 4m − 15 = 21
  11. 7n + 10 = 17
  12. 4y + 15 = 59

Equations with brackets

Class 7–8 · Worksheet 4 · set 7
Name:Date:Score:    / 10

Solve.

  1. 3(y + 3) = 18
  2. 2(x + 6) = 28
  3. 6(m − 5) + 2 = −22
  4. 2(y − 2) + 9 = 9
  5. 4(n − 2) + 7 = 47
  6. 6(n − 4) + 6 = 54
  7. 5(n − 4) + 12 = 22
  8. 6(n − 8) + 6 = −12
  9. 2(n + 3) = 8
  10. 4(x + 8) = 64

Variables on both sides

Class 8 · Worksheet 5 · set 7
Name:Date:Score:    / 10

Solve.

  1. 4x + 3 = x + 21
  2. 5n − 4 = 3n + 12
  3. 8y − 10 = 4y − 18
  4. 8m − 14 = 7m − 6
  5. 9x + 8 = 3x − 34
  6. 3n − 11 = n − 29
  7. 3n − 8 = 2n − 12
  8. 3y + 3 = y + 13
  9. 3x − 5 = x − 11
  10. 9m − 12 = 5m − 24

Equation word problems

Class 7–8 · Worksheet 6 · set 7
Name:Date:Score:    / 6

Form an equation and solve.

  1. The length of a rectangle is 5 cm more than its width. Its perimeter is 70 cm. Find the length and the width.
  2. I think of a number, multiply it by 4 and add 6. The answer is 78. What is the number?
  3. I think of a number, multiply it by 4 and add 6. The answer is 62. What is the number?
  4. I think of a number, multiply it by 4 and add 15. The answer is 79. What is the number?
  5. I think of a number, multiply it by 2 and add 10. The answer is 28. What is the number?
  6. The sum of two consecutive numbers is 25. Find the numbers.

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Questions

What is a linear equation in one variable?

An equation with one letter whose highest power is 1, such as 3x + 4 = 19. It has exactly one solution.

How do I solve word problems on simple equations?

Call the unknown x, write the sentence as an equation (“3 times a number plus 5 is 26” → 3x + 5 = 26), solve it, then check the answer in the story.

Are these worksheets free?

Yes — print them or save as PDF free. Every worksheet has an answer key.

How do I get different questions?

Press “🔄 New set” — the questions change (maths numbers are new every time; English sentences are shuffled).

How do I print only one worksheet?

Press “🖨️ Print” on that worksheet. Tick “with answer key” if you want the answers on a second page.

Can my child do this worksheet online, like a quiz?

Yes — press “▶️ Practise online” on any worksheet. The questions come one at a time with instant marking, a score at the end and a review of mistakes. No sign-in is needed.