Small practice. Bright discoveries.Explore the free starter collection
worksheetstudio.
Sign in
Back to worksheets
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.

New variationTry interactive challengeBrowse templates
Age band:Ages 13-15Ages 16-18

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 13-15

Linear equations

Take your time. Show your thinking.

  1. 1. Solve 2x + 6 = 24.

    LHS=RHS
    2 · 6 · 24 · Linear equations

  2. 2. Solve 10x + 27 = 207.

    LHS=RHS
    10 · 27 · 207 · Linear equations

  3. 3. Solve 12x + 26 = 110.

    LHS=RHS
    12 · 26 · 110 · Linear equations

  4. 4. Solve 6x + 4 = 10.

    LHS=RHS
    6 · 4 · 10 · Linear equations

  5. 5. Solve 5x + 18 = 63.

    LHS=RHS
    5 · 18 · 63 · Linear equations

  6. 6. Solve 4x + 26 = 106.

    LHS=RHS
    4 · 26 · 106 · Linear equations

  7. 7. Solve 8x + 18 = 98.

    LHS=RHS
    8 · 18 · 98 · Linear equations

  8. 8. Solve 8x + 22 = 142.

    LHS=RHS
    8 · 22 · 142 · Linear equations

  9. 9. Solve 3x + 24 = 51.

    LHS=RHS
    3 · 24 · 51 · Linear equations

  10. 10. Solve 3x + 15 = 75.

    LHS=RHS
    3 · 15 · 75 · Linear equations

  11. 11. Solve 8x + 3 = 123.

    LHS=RHS
    8 · 3 · 123 · Linear equations

  12. 12. Solve 6x + 6 = 60.

    LHS=RHS
    6 · 6 · 60 · Linear equations
12 questions · Seed 104731 · 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 2x + 6 = 24.

    9

    Subtract 6, then divide by 2. x = 9. Check: 2 × 9 + 6 = 24.

  2. 2. Solve 10x + 27 = 207.

    18

    Subtract 27, then divide by 10. x = 18. Check: 10 × 18 + 27 = 207.

  3. 3. Solve 12x + 26 = 110.

    7

    Subtract 26, then divide by 12. x = 7. Check: 12 × 7 + 26 = 110.

  4. 4. Solve 6x + 4 = 10.

    1

    Subtract 4, then divide by 6. x = 1. Check: 6 × 1 + 4 = 10.

  5. 5. Solve 5x + 18 = 63.

    9

    Subtract 18, then divide by 5. x = 9. Check: 5 × 9 + 18 = 63.

  6. 6. Solve 4x + 26 = 106.

    20

    Subtract 26, then divide by 4. x = 20. Check: 4 × 20 + 26 = 106.

  7. 7. Solve 8x + 18 = 98.

    10

    Subtract 18, then divide by 8. x = 10. Check: 8 × 10 + 18 = 98.

  8. 8. Solve 8x + 22 = 142.

    15

    Subtract 22, then divide by 8. x = 15. Check: 8 × 15 + 22 = 142.

  9. 9. Solve 3x + 24 = 51.

    9

    Subtract 24, then divide by 3. x = 9. Check: 3 × 9 + 24 = 51.

  10. 10. Solve 3x + 15 = 75.

    20

    Subtract 15, then divide by 3. x = 20. Check: 3 × 20 + 15 = 75.

  11. 11. Solve 8x + 3 = 123.

    15

    Subtract 3, then divide by 8. x = 15. Check: 8 × 15 + 3 = 123.

  12. 12. Solve 6x + 6 = 60.

    9

    Subtract 6, then divide by 6. x = 9. Check: 6 × 9 + 6 = 60.

12 questions · Seed 104731 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Linear equations

Take your time. Show your thinking.

  1. 1. Solve 2x + 6 = 24.

    LHS=RHS
    2 · 6 · 24 · Linear equations

  2. 2. Solve 10x + 27 = 207.

    LHS=RHS
    10 · 27 · 207 · Linear equations

  3. 3. Solve 12x + 26 = 110.

    LHS=RHS
    12 · 26 · 110 · Linear equations

  4. 4. Solve 6x + 4 = 10.

    LHS=RHS
    6 · 4 · 10 · Linear equations

  5. 5. Solve 5x + 18 = 63.

    LHS=RHS
    5 · 18 · 63 · Linear equations

  6. 6. Solve 4x + 26 = 106.

    LHS=RHS
    4 · 26 · 106 · Linear equations

  7. 7. Solve 8x + 18 = 98.

    LHS=RHS
    8 · 18 · 98 · Linear equations

  8. 8. Solve 8x + 22 = 142.

    LHS=RHS
    8 · 22 · 142 · Linear equations

  9. 9. Solve 3x + 24 = 51.

    LHS=RHS
    3 · 24 · 51 · Linear equations

  10. 10. Solve 3x + 15 = 75.

    LHS=RHS
    3 · 15 · 75 · Linear equations

  11. 11. Solve 8x + 3 = 123.

    LHS=RHS
    8 · 3 · 123 · Linear equations

  12. 12. Solve 6x + 6 = 60.

    LHS=RHS
    6 · 6 · 60 · Linear equations
12 questions · Seed 104731 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Linear equations

Answers and reasoning. Review before teaching.

  1. 1. Solve 2x + 6 = 24.

    9

    Subtract 6, then divide by 2. x = 9. Check: 2 × 9 + 6 = 24.

  2. 2. Solve 10x + 27 = 207.

    18

    Subtract 27, then divide by 10. x = 18. Check: 10 × 18 + 27 = 207.

  3. 3. Solve 12x + 26 = 110.

    7

    Subtract 26, then divide by 12. x = 7. Check: 12 × 7 + 26 = 110.

  4. 4. Solve 6x + 4 = 10.

    1

    Subtract 4, then divide by 6. x = 1. Check: 6 × 1 + 4 = 10.

  5. 5. Solve 5x + 18 = 63.

    9

    Subtract 18, then divide by 5. x = 9. Check: 5 × 9 + 18 = 63.

  6. 6. Solve 4x + 26 = 106.

    20

    Subtract 26, then divide by 4. x = 20. Check: 4 × 20 + 26 = 106.

  7. 7. Solve 8x + 18 = 98.

    10

    Subtract 18, then divide by 8. x = 10. Check: 8 × 10 + 18 = 98.

  8. 8. Solve 8x + 22 = 142.

    15

    Subtract 22, then divide by 8. x = 15. Check: 8 × 15 + 22 = 142.

  9. 9. Solve 3x + 24 = 51.

    9

    Subtract 24, then divide by 3. x = 9. Check: 3 × 9 + 24 = 51.

  10. 10. Solve 3x + 15 = 75.

    20

    Subtract 15, then divide by 3. x = 20. Check: 3 × 20 + 15 = 75.

  11. 11. Solve 8x + 3 = 123.

    15

    Subtract 3, then divide by 8. x = 15. Check: 8 × 15 + 3 = 123.

  12. 12. Solve 6x + 6 = 60.

    9

    Subtract 6, then divide by 6. x = 9. Check: 6 × 9 + 6 = 60.

12 questions · Seed 104731 · Age guidance, not curriculum certification