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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 4x + 21 = 33.

    LHS=RHS
    4 · 21 · 33 · Linear equations

  2. 2. Solve 5x + 16 = 106.

    LHS=RHS
    5 · 16 · 106 · Linear equations

  3. 3. Solve 12x + 1 = 73.

    LHS=RHS
    12 · 1 · 73 · Linear equations

  4. 4. Solve 5x + 5 = 10.

    LHS=RHS
    5 · 5 · 10 · Linear equations

  5. 5. Solve 6x + 28 = 40.

    LHS=RHS
    6 · 28 · 40 · Linear equations

  6. 6. Solve 12x + 28 = 64.

    LHS=RHS
    12 · 28 · 64 · Linear equations

  7. 7. Solve 2x + 17 = 29.

    LHS=RHS
    2 · 17 · 29 · Linear equations

  8. 8. Solve 11x + 29 = 150.

    LHS=RHS
    11 · 29 · 150 · Linear equations

  9. 9. Solve 6x + 5 = 59.

    LHS=RHS
    6 · 5 · 59 · Linear equations

  10. 10. Solve 7x + 8 = 29.

    LHS=RHS
    7 · 8 · 29 · Linear equations

  11. 11. Solve 9x + 26 = 62.

    LHS=RHS
    9 · 26 · 62 · Linear equations

  12. 12. Solve 11x + 7 = 106.

    LHS=RHS
    11 · 7 · 106 · Linear equations
12 questions · Seed 47 · 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 4x + 21 = 33.

    3

    Subtract 21, then divide by 4. x = 3. Check: 4 × 3 + 21 = 33.

  2. 2. Solve 5x + 16 = 106.

    18

    Subtract 16, then divide by 5. x = 18. Check: 5 × 18 + 16 = 106.

  3. 3. Solve 12x + 1 = 73.

    6

    Subtract 1, then divide by 12. x = 6. Check: 12 × 6 + 1 = 73.

  4. 4. Solve 5x + 5 = 10.

    1

    Subtract 5, then divide by 5. x = 1. Check: 5 × 1 + 5 = 10.

  5. 5. Solve 6x + 28 = 40.

    2

    Subtract 28, then divide by 6. x = 2. Check: 6 × 2 + 28 = 40.

  6. 6. Solve 12x + 28 = 64.

    3

    Subtract 28, then divide by 12. x = 3. Check: 12 × 3 + 28 = 64.

  7. 7. Solve 2x + 17 = 29.

    6

    Subtract 17, then divide by 2. x = 6. Check: 2 × 6 + 17 = 29.

  8. 8. Solve 11x + 29 = 150.

    11

    Subtract 29, then divide by 11. x = 11. Check: 11 × 11 + 29 = 150.

  9. 9. Solve 6x + 5 = 59.

    9

    Subtract 5, then divide by 6. x = 9. Check: 6 × 9 + 5 = 59.

  10. 10. Solve 7x + 8 = 29.

    3

    Subtract 8, then divide by 7. x = 3. Check: 7 × 3 + 8 = 29.

  11. 11. Solve 9x + 26 = 62.

    4

    Subtract 26, then divide by 9. x = 4. Check: 9 × 4 + 26 = 62.

  12. 12. Solve 11x + 7 = 106.

    9

    Subtract 7, then divide by 11. x = 9. Check: 11 × 9 + 7 = 106.

12 questions · Seed 47 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Linear equations

Take your time. Show your thinking.

  1. 1. Solve 4x + 21 = 33.

    LHS=RHS
    4 · 21 · 33 · Linear equations

  2. 2. Solve 5x + 16 = 106.

    LHS=RHS
    5 · 16 · 106 · Linear equations

  3. 3. Solve 12x + 1 = 73.

    LHS=RHS
    12 · 1 · 73 · Linear equations

  4. 4. Solve 5x + 5 = 10.

    LHS=RHS
    5 · 5 · 10 · Linear equations

  5. 5. Solve 6x + 28 = 40.

    LHS=RHS
    6 · 28 · 40 · Linear equations

  6. 6. Solve 12x + 28 = 64.

    LHS=RHS
    12 · 28 · 64 · Linear equations

  7. 7. Solve 2x + 17 = 29.

    LHS=RHS
    2 · 17 · 29 · Linear equations

  8. 8. Solve 11x + 29 = 150.

    LHS=RHS
    11 · 29 · 150 · Linear equations

  9. 9. Solve 6x + 5 = 59.

    LHS=RHS
    6 · 5 · 59 · Linear equations

  10. 10. Solve 7x + 8 = 29.

    LHS=RHS
    7 · 8 · 29 · Linear equations

  11. 11. Solve 9x + 26 = 62.

    LHS=RHS
    9 · 26 · 62 · Linear equations

  12. 12. Solve 11x + 7 = 106.

    LHS=RHS
    11 · 7 · 106 · Linear equations
12 questions · Seed 47 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Linear equations

Answers and reasoning. Review before teaching.

  1. 1. Solve 4x + 21 = 33.

    3

    Subtract 21, then divide by 4. x = 3. Check: 4 × 3 + 21 = 33.

  2. 2. Solve 5x + 16 = 106.

    18

    Subtract 16, then divide by 5. x = 18. Check: 5 × 18 + 16 = 106.

  3. 3. Solve 12x + 1 = 73.

    6

    Subtract 1, then divide by 12. x = 6. Check: 12 × 6 + 1 = 73.

  4. 4. Solve 5x + 5 = 10.

    1

    Subtract 5, then divide by 5. x = 1. Check: 5 × 1 + 5 = 10.

  5. 5. Solve 6x + 28 = 40.

    2

    Subtract 28, then divide by 6. x = 2. Check: 6 × 2 + 28 = 40.

  6. 6. Solve 12x + 28 = 64.

    3

    Subtract 28, then divide by 12. x = 3. Check: 12 × 3 + 28 = 64.

  7. 7. Solve 2x + 17 = 29.

    6

    Subtract 17, then divide by 2. x = 6. Check: 2 × 6 + 17 = 29.

  8. 8. Solve 11x + 29 = 150.

    11

    Subtract 29, then divide by 11. x = 11. Check: 11 × 11 + 29 = 150.

  9. 9. Solve 6x + 5 = 59.

    9

    Subtract 5, then divide by 6. x = 9. Check: 6 × 9 + 5 = 59.

  10. 10. Solve 7x + 8 = 29.

    3

    Subtract 8, then divide by 7. x = 3. Check: 7 × 3 + 8 = 29.

  11. 11. Solve 9x + 26 = 62.

    4

    Subtract 26, then divide by 9. x = 4. Check: 9 × 4 + 26 = 62.

  12. 12. Solve 11x + 7 = 106.

    9

    Subtract 7, then divide by 11. x = 9. Check: 11 × 9 + 7 = 106.

12 questions · Seed 47 · Age guidance, not curriculum certification