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MathsAges 13-15

Linear equations

Solve a linear equation by reversing addition and multiplication, then substitute your answer to check it. Review suitability for your learners before teaching.

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Age band:Ages 13-15Ages 16-18

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Worksheet StudioPractice pack · Ages 13-15

Linear equations

Take your time. Show your thinking.

  1. 1. Solve 10x + 2 = 162.

    LHS=RHS
    10 · 2 · 162 · Linear equations

  2. 2. Solve 6x + 9 = 39.

    LHS=RHS
    6 · 9 · 39 · Linear equations

  3. 3. Solve 7x + 3 = 10.

    LHS=RHS
    7 · 3 · 10 · Linear equations

  4. 4. Solve 12x + 28 = 208.

    LHS=RHS
    12 · 28 · 208 · Linear equations

  5. 5. Solve 2x + 8 = 14.

    LHS=RHS
    2 · 8 · 14 · Linear equations

  6. 6. Solve 4x + 5 = 45.

    LHS=RHS
    4 · 5 · 45 · Linear equations

  7. 7. Solve 4x + 28 = 32.

    LHS=RHS
    4 · 28 · 32 · Linear equations

  8. 8. Solve 4x + 4 = 84.

    LHS=RHS
    4 · 4 · 84 · Linear equations

  9. 9. Solve 6x + 19 = 127.

    LHS=RHS
    6 · 19 · 127 · Linear equations

  10. 10. Solve 7x + 22 = 92.

    LHS=RHS
    7 · 22 · 92 · Linear equations

  11. 11. Solve 3x + 22 = 82.

    LHS=RHS
    3 · 22 · 82 · Linear equations

  12. 12. Solve 7x + 21 = 91.

    LHS=RHS
    7 · 21 · 91 · Linear equations
12 questions · Seed 43 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 13-15

Linear equations

Answers and reasoning. Review before teaching.

  1. 1. Solve 10x + 2 = 162.

    16

    Subtract 2, then divide by 10. x = 16. Check: 10 × 16 + 2 = 162.

  2. 2. Solve 6x + 9 = 39.

    5

    Subtract 9, then divide by 6. x = 5. Check: 6 × 5 + 9 = 39.

  3. 3. Solve 7x + 3 = 10.

    1

    Subtract 3, then divide by 7. x = 1. Check: 7 × 1 + 3 = 10.

  4. 4. Solve 12x + 28 = 208.

    15

    Subtract 28, then divide by 12. x = 15. Check: 12 × 15 + 28 = 208.

  5. 5. Solve 2x + 8 = 14.

    3

    Subtract 8, then divide by 2. x = 3. Check: 2 × 3 + 8 = 14.

  6. 6. Solve 4x + 5 = 45.

    10

    Subtract 5, then divide by 4. x = 10. Check: 4 × 10 + 5 = 45.

  7. 7. Solve 4x + 28 = 32.

    1

    Subtract 28, then divide by 4. x = 1. Check: 4 × 1 + 28 = 32.

  8. 8. Solve 4x + 4 = 84.

    20

    Subtract 4, then divide by 4. x = 20. Check: 4 × 20 + 4 = 84.

  9. 9. Solve 6x + 19 = 127.

    18

    Subtract 19, then divide by 6. x = 18. Check: 6 × 18 + 19 = 127.

  10. 10. Solve 7x + 22 = 92.

    10

    Subtract 22, then divide by 7. x = 10. Check: 7 × 10 + 22 = 92.

  11. 11. Solve 3x + 22 = 82.

    20

    Subtract 22, then divide by 3. x = 20. Check: 3 × 20 + 22 = 82.

  12. 12. Solve 7x + 21 = 91.

    10

    Subtract 21, then divide by 7. x = 10. Check: 7 × 10 + 21 = 91.

12 questions · Seed 43 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Linear equations

Take your time. Show your thinking.

  1. 1. Solve 10x + 2 = 162.

    LHS=RHS
    10 · 2 · 162 · Linear equations

  2. 2. Solve 6x + 9 = 39.

    LHS=RHS
    6 · 9 · 39 · Linear equations

  3. 3. Solve 7x + 3 = 10.

    LHS=RHS
    7 · 3 · 10 · Linear equations

  4. 4. Solve 12x + 28 = 208.

    LHS=RHS
    12 · 28 · 208 · Linear equations

  5. 5. Solve 2x + 8 = 14.

    LHS=RHS
    2 · 8 · 14 · Linear equations

  6. 6. Solve 4x + 5 = 45.

    LHS=RHS
    4 · 5 · 45 · Linear equations

  7. 7. Solve 4x + 28 = 32.

    LHS=RHS
    4 · 28 · 32 · Linear equations

  8. 8. Solve 4x + 4 = 84.

    LHS=RHS
    4 · 4 · 84 · Linear equations

  9. 9. Solve 6x + 19 = 127.

    LHS=RHS
    6 · 19 · 127 · Linear equations

  10. 10. Solve 7x + 22 = 92.

    LHS=RHS
    7 · 22 · 92 · Linear equations

  11. 11. Solve 3x + 22 = 82.

    LHS=RHS
    3 · 22 · 82 · Linear equations

  12. 12. Solve 7x + 21 = 91.

    LHS=RHS
    7 · 21 · 91 · Linear equations
12 questions · Seed 43 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Linear equations

Answers and reasoning. Review before teaching.

  1. 1. Solve 10x + 2 = 162.

    16

    Subtract 2, then divide by 10. x = 16. Check: 10 × 16 + 2 = 162.

  2. 2. Solve 6x + 9 = 39.

    5

    Subtract 9, then divide by 6. x = 5. Check: 6 × 5 + 9 = 39.

  3. 3. Solve 7x + 3 = 10.

    1

    Subtract 3, then divide by 7. x = 1. Check: 7 × 1 + 3 = 10.

  4. 4. Solve 12x + 28 = 208.

    15

    Subtract 28, then divide by 12. x = 15. Check: 12 × 15 + 28 = 208.

  5. 5. Solve 2x + 8 = 14.

    3

    Subtract 8, then divide by 2. x = 3. Check: 2 × 3 + 8 = 14.

  6. 6. Solve 4x + 5 = 45.

    10

    Subtract 5, then divide by 4. x = 10. Check: 4 × 10 + 5 = 45.

  7. 7. Solve 4x + 28 = 32.

    1

    Subtract 28, then divide by 4. x = 1. Check: 4 × 1 + 28 = 32.

  8. 8. Solve 4x + 4 = 84.

    20

    Subtract 4, then divide by 4. x = 20. Check: 4 × 20 + 4 = 84.

  9. 9. Solve 6x + 19 = 127.

    18

    Subtract 19, then divide by 6. x = 18. Check: 6 × 18 + 19 = 127.

  10. 10. Solve 7x + 22 = 92.

    10

    Subtract 22, then divide by 7. x = 10. Check: 7 × 10 + 22 = 92.

  11. 11. Solve 3x + 22 = 82.

    20

    Subtract 22, then divide by 3. x = 20. Check: 3 × 20 + 22 = 82.

  12. 12. Solve 7x + 21 = 91.

    10

    Subtract 21, then divide by 7. x = 10. Check: 7 × 10 + 21 = 91.

12 questions · Seed 43 · Age guidance, not curriculum certification