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Free · Class 6–8 · 6 worksheets · answer keys · practise online · set 45

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 45
Name:Date:Score:    / 12

Solve.

  1. n − 14 = 8
  2. 11 + m = 20
  3. n − 2 = 22
  4. 4 + n = 25
  5. 17 + m = 33
  6. p + 7 = 29
  7. 17 + m = 26
  8. n + 27 = 28
  9. p + 3 = 6
  10. 5 + p = 22
  11. p − 18 = 4
  12. n + 14 = 15

One-step equations (× and ÷)

Class 6–7 · Worksheet 2 · set 45
Name:Date:Score:    / 12

Solve.

  1. 3p = 42
  2. 3m = 24
  3. y/3 = 3
  4. 4p = 52
  5. y/2 = 8
  6. 7n = 105
  7. p/7 = 10
  8. x/3 = 2
  9. 4n = 32
  10. y/3 = 12
  11. x/7 = 8
  12. n/5 = 5

Two-step equations

Class 7 · Worksheet 3 · set 45
Name:Date:Score:    / 12

Solve.

  1. 5m − 1 = 24
  2. 7x − 9 = 33
  3. 3n + 16 = 22
  4. 7y + 1 = 22
  5. 8m + 6 = 22
  6. 8p + 2 = 74
  7. 2x + 14 = 18
  8. 4y + 2 = 38
  9. 8y + 1 = 33
  10. 2x + 9 = 27
  11. 6x − 6 = 24
  12. 3n − 3 = 15

Equations with brackets

Class 7–8 · Worksheet 4 · set 45
Name:Date:Score:    / 10

Solve.

  1. 4(m − 4) + 2 = 22
  2. 4(y − 3) + 13 = 49
  3. 2(m + 2) = 20
  4. 6(x − 6) + 6 = −24
  5. 3(x + 2) = 15
  6. 3(m − 2) + 11 = 35
  7. 6(y + 2) = 78
  8. 6(x − 4) + 10 = 40
  9. 5(n − 5) + 7 = 2
  10. 3(m − 9) + 14 = −1

Variables on both sides

Class 8 · Worksheet 5 · set 45
Name:Date:Score:    / 10

Solve.

  1. 6y − 9 = 4y − 19
  2. 4x + 10 = 3x + 13
  3. 6n − 14 = 5n − 15
  4. 4y − 16 = 2y − 18
  5. 3m + 15 = 2m + 21
  6. 7y − 14 = 2y − 54
  7. 9x − 14 = 5x + 14
  8. 4m − 11 = m − 29
  9. 6y − 17 = 5y − 11
  10. 7n + 8 = n − 46

Equation word problems

Class 7–8 · Worksheet 6 · set 45
Name:Date:Score:    / 6

Form an equation and solve.

  1. The length of a rectangle is 8 cm more than its width. Its perimeter is 36 cm. Find the length and the width.
  2. Ravi has ₹37 more than Asha. Together they have ₹417. How much money does Asha have?
  3. The length of a rectangle is 7 cm more than its width. Its perimeter is 66 cm. Find the length and the width.
  4. A father is 4 times as old as his son. The sum of their ages is 25 years. Find their ages.
  5. Ravi has ₹5 more than Asha. Together they have ₹81. How much money does Asha have?
  6. Ravi has ₹46 more than Asha. Together they have ₹344. How much money does Asha have?

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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).

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

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