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MathsAges 13-15

Equations with brackets & fractions

Solve multi-step linear equations involving bracketed expressions and algebraic fractions by clearing the denominator. 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

Equations with brackets & fractions

Take your time. Show your thinking.

  1. 1. Solve the algebraic fraction equation 6(x + 4) ÷ 2 = 36 for x.

    LHS=RHS
    6(x + 4) ÷ 2 = 36 · x + 4 = 12 → x = ?

  2. 2. Solve the algebraic fraction equation 5(x + 10) ÷ 4 = 25 for x.

    LHS=RHS
    5(x + 10) ÷ 4 = 25 · x + 10 = 20 → x = ?

  3. 3. Solve the algebraic fraction equation 4(x + 26) ÷ 4 = 52 for x.

    LHS=RHS
    4(x + 26) ÷ 4 = 52 · x + 26 = 52 → x = ?

  4. 4. Solve the algebraic fraction equation 6(x + 30) ÷ 7 = 60 for x.

    LHS=RHS
    6(x + 30) ÷ 7 = 60 · x + 30 = 70 → x = ?

  5. 5. Solve the algebraic fraction equation 2(x + 6) ÷ 4 = 8 for x.

    LHS=RHS
    2(x + 6) ÷ 4 = 8 · x + 6 = 16 → x = ?

  6. 6. Solve the algebraic fraction equation 2(x + 18) ÷ 7 = 22 for x.

    LHS=RHS
    2(x + 18) ÷ 7 = 22 · x + 18 = 77 → x = ?

  7. 7. Solve the algebraic fraction equation 3(x + 5) ÷ 6 = 39 for x.

    LHS=RHS
    3(x + 5) ÷ 6 = 39 · x + 5 = 78 → x = ?

  8. 8. Solve the algebraic fraction equation 3(x + 3) ÷ 2 = 24 for x.

    LHS=RHS
    3(x + 3) ÷ 2 = 24 · x + 3 = 16 → x = ?

  9. 9. Solve the algebraic fraction equation 2(x + 58) ÷ 6 = 26 for x.

    LHS=RHS
    2(x + 58) ÷ 6 = 26 · x + 58 = 78 → x = ?

  10. 10. Solve the algebraic fraction equation 5(x + 9) ÷ 2 = 40 for x.

    LHS=RHS
    5(x + 9) ÷ 2 = 40 · x + 9 = 16 → x = ?

  11. 11. Solve the algebraic fraction equation 3(x + 1) ÷ 3 = 12 for x.

    LHS=RHS
    3(x + 1) ÷ 3 = 12 · x + 1 = 12 → x = ?

  12. 12. Solve the algebraic fraction equation 4(x + 14) ÷ 3 = 24 for x.

    LHS=RHS
    4(x + 14) ÷ 3 = 24 · x + 14 = 18 → x = ?
12 questions · Seed 45 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 13-15

Equations with brackets & fractions

Answers and reasoning. Review before teaching.

  1. 1. Solve the algebraic fraction equation 6(x + 4) ÷ 2 = 36 for x.

    8

    Multiply both sides by 2 to get 6(x + 4) = 72. Divide by 6 to get x + 4 = 12, so x = 8.

  2. 2. Solve the algebraic fraction equation 5(x + 10) ÷ 4 = 25 for x.

    10

    Multiply both sides by 4 to get 5(x + 10) = 100. Divide by 5 to get x + 10 = 20, so x = 10.

  3. 3. Solve the algebraic fraction equation 4(x + 26) ÷ 4 = 52 for x.

    26

    Multiply both sides by 4 to get 4(x + 26) = 208. Divide by 4 to get x + 26 = 52, so x = 26.

  4. 4. Solve the algebraic fraction equation 6(x + 30) ÷ 7 = 60 for x.

    40

    Multiply both sides by 7 to get 6(x + 30) = 420. Divide by 6 to get x + 30 = 70, so x = 40.

  5. 5. Solve the algebraic fraction equation 2(x + 6) ÷ 4 = 8 for x.

    10

    Multiply both sides by 4 to get 2(x + 6) = 32. Divide by 2 to get x + 6 = 16, so x = 10.

  6. 6. Solve the algebraic fraction equation 2(x + 18) ÷ 7 = 22 for x.

    59

    Multiply both sides by 7 to get 2(x + 18) = 154. Divide by 2 to get x + 18 = 77, so x = 59.

  7. 7. Solve the algebraic fraction equation 3(x + 5) ÷ 6 = 39 for x.

    73

    Multiply both sides by 6 to get 3(x + 5) = 234. Divide by 3 to get x + 5 = 78, so x = 73.

  8. 8. Solve the algebraic fraction equation 3(x + 3) ÷ 2 = 24 for x.

    13

    Multiply both sides by 2 to get 3(x + 3) = 48. Divide by 3 to get x + 3 = 16, so x = 13.

  9. 9. Solve the algebraic fraction equation 2(x + 58) ÷ 6 = 26 for x.

    20

    Multiply both sides by 6 to get 2(x + 58) = 156. Divide by 2 to get x + 58 = 78, so x = 20.

  10. 10. Solve the algebraic fraction equation 5(x + 9) ÷ 2 = 40 for x.

    7

    Multiply both sides by 2 to get 5(x + 9) = 80. Divide by 5 to get x + 9 = 16, so x = 7.

  11. 11. Solve the algebraic fraction equation 3(x + 1) ÷ 3 = 12 for x.

    11

    Multiply both sides by 3 to get 3(x + 1) = 36. Divide by 3 to get x + 1 = 12, so x = 11.

  12. 12. Solve the algebraic fraction equation 4(x + 14) ÷ 3 = 24 for x.

    4

    Multiply both sides by 3 to get 4(x + 14) = 72. Divide by 4 to get x + 14 = 18, so x = 4.

12 questions · Seed 45 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Equations with brackets & fractions

Take your time. Show your thinking.

  1. 1. Solve the algebraic fraction equation 6(x + 4) ÷ 2 = 36 for x.

    LHS=RHS
    6(x + 4) ÷ 2 = 36 · x + 4 = 12 → x = ?

  2. 2. Solve the algebraic fraction equation 5(x + 10) ÷ 4 = 25 for x.

    LHS=RHS
    5(x + 10) ÷ 4 = 25 · x + 10 = 20 → x = ?

  3. 3. Solve the algebraic fraction equation 4(x + 26) ÷ 4 = 52 for x.

    LHS=RHS
    4(x + 26) ÷ 4 = 52 · x + 26 = 52 → x = ?

  4. 4. Solve the algebraic fraction equation 6(x + 30) ÷ 7 = 60 for x.

    LHS=RHS
    6(x + 30) ÷ 7 = 60 · x + 30 = 70 → x = ?

  5. 5. Solve the algebraic fraction equation 2(x + 6) ÷ 4 = 8 for x.

    LHS=RHS
    2(x + 6) ÷ 4 = 8 · x + 6 = 16 → x = ?

  6. 6. Solve the algebraic fraction equation 2(x + 18) ÷ 7 = 22 for x.

    LHS=RHS
    2(x + 18) ÷ 7 = 22 · x + 18 = 77 → x = ?

  7. 7. Solve the algebraic fraction equation 3(x + 5) ÷ 6 = 39 for x.

    LHS=RHS
    3(x + 5) ÷ 6 = 39 · x + 5 = 78 → x = ?

  8. 8. Solve the algebraic fraction equation 3(x + 3) ÷ 2 = 24 for x.

    LHS=RHS
    3(x + 3) ÷ 2 = 24 · x + 3 = 16 → x = ?

  9. 9. Solve the algebraic fraction equation 2(x + 58) ÷ 6 = 26 for x.

    LHS=RHS
    2(x + 58) ÷ 6 = 26 · x + 58 = 78 → x = ?

  10. 10. Solve the algebraic fraction equation 5(x + 9) ÷ 2 = 40 for x.

    LHS=RHS
    5(x + 9) ÷ 2 = 40 · x + 9 = 16 → x = ?

  11. 11. Solve the algebraic fraction equation 3(x + 1) ÷ 3 = 12 for x.

    LHS=RHS
    3(x + 1) ÷ 3 = 12 · x + 1 = 12 → x = ?

  12. 12. Solve the algebraic fraction equation 4(x + 14) ÷ 3 = 24 for x.

    LHS=RHS
    4(x + 14) ÷ 3 = 24 · x + 14 = 18 → x = ?
12 questions · Seed 45 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Equations with brackets & fractions

Answers and reasoning. Review before teaching.

  1. 1. Solve the algebraic fraction equation 6(x + 4) ÷ 2 = 36 for x.

    8

    Multiply both sides by 2 to get 6(x + 4) = 72. Divide by 6 to get x + 4 = 12, so x = 8.

  2. 2. Solve the algebraic fraction equation 5(x + 10) ÷ 4 = 25 for x.

    10

    Multiply both sides by 4 to get 5(x + 10) = 100. Divide by 5 to get x + 10 = 20, so x = 10.

  3. 3. Solve the algebraic fraction equation 4(x + 26) ÷ 4 = 52 for x.

    26

    Multiply both sides by 4 to get 4(x + 26) = 208. Divide by 4 to get x + 26 = 52, so x = 26.

  4. 4. Solve the algebraic fraction equation 6(x + 30) ÷ 7 = 60 for x.

    40

    Multiply both sides by 7 to get 6(x + 30) = 420. Divide by 6 to get x + 30 = 70, so x = 40.

  5. 5. Solve the algebraic fraction equation 2(x + 6) ÷ 4 = 8 for x.

    10

    Multiply both sides by 4 to get 2(x + 6) = 32. Divide by 2 to get x + 6 = 16, so x = 10.

  6. 6. Solve the algebraic fraction equation 2(x + 18) ÷ 7 = 22 for x.

    59

    Multiply both sides by 7 to get 2(x + 18) = 154. Divide by 2 to get x + 18 = 77, so x = 59.

  7. 7. Solve the algebraic fraction equation 3(x + 5) ÷ 6 = 39 for x.

    73

    Multiply both sides by 6 to get 3(x + 5) = 234. Divide by 3 to get x + 5 = 78, so x = 73.

  8. 8. Solve the algebraic fraction equation 3(x + 3) ÷ 2 = 24 for x.

    13

    Multiply both sides by 2 to get 3(x + 3) = 48. Divide by 3 to get x + 3 = 16, so x = 13.

  9. 9. Solve the algebraic fraction equation 2(x + 58) ÷ 6 = 26 for x.

    20

    Multiply both sides by 6 to get 2(x + 58) = 156. Divide by 2 to get x + 58 = 78, so x = 20.

  10. 10. Solve the algebraic fraction equation 5(x + 9) ÷ 2 = 40 for x.

    7

    Multiply both sides by 2 to get 5(x + 9) = 80. Divide by 5 to get x + 9 = 16, so x = 7.

  11. 11. Solve the algebraic fraction equation 3(x + 1) ÷ 3 = 12 for x.

    11

    Multiply both sides by 3 to get 3(x + 1) = 36. Divide by 3 to get x + 1 = 12, so x = 11.

  12. 12. Solve the algebraic fraction equation 4(x + 14) ÷ 3 = 24 for x.

    4

    Multiply both sides by 3 to get 4(x + 14) = 72. Divide by 4 to get x + 14 = 18, so x = 4.

12 questions · Seed 45 · Age guidance, not curriculum certification