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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 3(x + 9) ÷ 7 = 9 for x.

    LHS=RHS
    3(x + 9) ÷ 7 = 9 · x + 9 = 21 → x = ?

  2. 2. Solve the algebraic fraction equation 6(x + 38) ÷ 3 = 84 for x.

    LHS=RHS
    6(x + 38) ÷ 3 = 84 · x + 38 = 42 → x = ?

  3. 3. Solve the algebraic fraction equation 5(x + 38) ÷ 5 = 65 for x.

    LHS=RHS
    5(x + 38) ÷ 5 = 65 · x + 38 = 65 → x = ?

  4. 4. Solve the algebraic fraction equation 5(x + 12) ÷ 5 = 25 for x.

    LHS=RHS
    5(x + 12) ÷ 5 = 25 · x + 12 = 25 → x = ?

  5. 5. Solve the algebraic fraction equation 5(x + 9) ÷ 5 = 50 for x.

    LHS=RHS
    5(x + 9) ÷ 5 = 50 · x + 9 = 50 → x = ?

  6. 6. Solve the algebraic fraction equation 6(x + 3) ÷ 2 = 18 for x.

    LHS=RHS
    6(x + 3) ÷ 2 = 18 · x + 3 = 6 → x = ?

  7. 7. Solve the algebraic fraction equation 4(x + 17) ÷ 2 = 44 for x.

    LHS=RHS
    4(x + 17) ÷ 2 = 44 · x + 17 = 22 → x = ?

  8. 8. Solve the algebraic fraction equation 6(x + 9) ÷ 2 = 78 for x.

    LHS=RHS
    6(x + 9) ÷ 2 = 78 · x + 9 = 26 → x = ?

  9. 9. Solve the algebraic fraction equation 2(x + 5) ÷ 7 = 18 for x.

    LHS=RHS
    2(x + 5) ÷ 7 = 18 · x + 5 = 63 → x = ?

  10. 10. Solve the algebraic fraction equation 4(x + 10) ÷ 4 = 32 for x.

    LHS=RHS
    4(x + 10) ÷ 4 = 32 · x + 10 = 32 → x = ?

  11. 11. Solve the algebraic fraction equation 4(x + 1) ÷ 2 = 16 for x.

    LHS=RHS
    4(x + 1) ÷ 2 = 16 · x + 1 = 8 → x = ?

  12. 12. Solve the algebraic fraction equation 4(x + 57) ÷ 6 = 44 for x.

    LHS=RHS
    4(x + 57) ÷ 6 = 44 · x + 57 = 66 → x = ?
12 questions · Seed 43 · 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 3(x + 9) ÷ 7 = 9 for x.

    12

    Multiply both sides by 7 to get 3(x + 9) = 63. Divide by 3 to get x + 9 = 21, so x = 12.

  2. 2. Solve the algebraic fraction equation 6(x + 38) ÷ 3 = 84 for x.

    4

    Multiply both sides by 3 to get 6(x + 38) = 252. Divide by 6 to get x + 38 = 42, so x = 4.

  3. 3. Solve the algebraic fraction equation 5(x + 38) ÷ 5 = 65 for x.

    27

    Multiply both sides by 5 to get 5(x + 38) = 325. Divide by 5 to get x + 38 = 65, so x = 27.

  4. 4. Solve the algebraic fraction equation 5(x + 12) ÷ 5 = 25 for x.

    13

    Multiply both sides by 5 to get 5(x + 12) = 125. Divide by 5 to get x + 12 = 25, so x = 13.

  5. 5. Solve the algebraic fraction equation 5(x + 9) ÷ 5 = 50 for x.

    41

    Multiply both sides by 5 to get 5(x + 9) = 250. Divide by 5 to get x + 9 = 50, so x = 41.

  6. 6. Solve the algebraic fraction equation 6(x + 3) ÷ 2 = 18 for x.

    3

    Multiply both sides by 2 to get 6(x + 3) = 36. Divide by 6 to get x + 3 = 6, so x = 3.

  7. 7. Solve the algebraic fraction equation 4(x + 17) ÷ 2 = 44 for x.

    5

    Multiply both sides by 2 to get 4(x + 17) = 88. Divide by 4 to get x + 17 = 22, so x = 5.

  8. 8. Solve the algebraic fraction equation 6(x + 9) ÷ 2 = 78 for x.

    17

    Multiply both sides by 2 to get 6(x + 9) = 156. Divide by 6 to get x + 9 = 26, so x = 17.

  9. 9. Solve the algebraic fraction equation 2(x + 5) ÷ 7 = 18 for x.

    58

    Multiply both sides by 7 to get 2(x + 5) = 126. Divide by 2 to get x + 5 = 63, so x = 58.

  10. 10. Solve the algebraic fraction equation 4(x + 10) ÷ 4 = 32 for x.

    22

    Multiply both sides by 4 to get 4(x + 10) = 128. Divide by 4 to get x + 10 = 32, so x = 22.

  11. 11. Solve the algebraic fraction equation 4(x + 1) ÷ 2 = 16 for x.

    7

    Multiply both sides by 2 to get 4(x + 1) = 32. Divide by 4 to get x + 1 = 8, so x = 7.

  12. 12. Solve the algebraic fraction equation 4(x + 57) ÷ 6 = 44 for x.

    9

    Multiply both sides by 6 to get 4(x + 57) = 264. Divide by 4 to get x + 57 = 66, so x = 9.

12 questions · Seed 43 · 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 3(x + 9) ÷ 7 = 9 for x.

    LHS=RHS
    3(x + 9) ÷ 7 = 9 · x + 9 = 21 → x = ?

  2. 2. Solve the algebraic fraction equation 6(x + 38) ÷ 3 = 84 for x.

    LHS=RHS
    6(x + 38) ÷ 3 = 84 · x + 38 = 42 → x = ?

  3. 3. Solve the algebraic fraction equation 5(x + 38) ÷ 5 = 65 for x.

    LHS=RHS
    5(x + 38) ÷ 5 = 65 · x + 38 = 65 → x = ?

  4. 4. Solve the algebraic fraction equation 5(x + 12) ÷ 5 = 25 for x.

    LHS=RHS
    5(x + 12) ÷ 5 = 25 · x + 12 = 25 → x = ?

  5. 5. Solve the algebraic fraction equation 5(x + 9) ÷ 5 = 50 for x.

    LHS=RHS
    5(x + 9) ÷ 5 = 50 · x + 9 = 50 → x = ?

  6. 6. Solve the algebraic fraction equation 6(x + 3) ÷ 2 = 18 for x.

    LHS=RHS
    6(x + 3) ÷ 2 = 18 · x + 3 = 6 → x = ?

  7. 7. Solve the algebraic fraction equation 4(x + 17) ÷ 2 = 44 for x.

    LHS=RHS
    4(x + 17) ÷ 2 = 44 · x + 17 = 22 → x = ?

  8. 8. Solve the algebraic fraction equation 6(x + 9) ÷ 2 = 78 for x.

    LHS=RHS
    6(x + 9) ÷ 2 = 78 · x + 9 = 26 → x = ?

  9. 9. Solve the algebraic fraction equation 2(x + 5) ÷ 7 = 18 for x.

    LHS=RHS
    2(x + 5) ÷ 7 = 18 · x + 5 = 63 → x = ?

  10. 10. Solve the algebraic fraction equation 4(x + 10) ÷ 4 = 32 for x.

    LHS=RHS
    4(x + 10) ÷ 4 = 32 · x + 10 = 32 → x = ?

  11. 11. Solve the algebraic fraction equation 4(x + 1) ÷ 2 = 16 for x.

    LHS=RHS
    4(x + 1) ÷ 2 = 16 · x + 1 = 8 → x = ?

  12. 12. Solve the algebraic fraction equation 4(x + 57) ÷ 6 = 44 for x.

    LHS=RHS
    4(x + 57) ÷ 6 = 44 · x + 57 = 66 → x = ?
12 questions · Seed 43 · 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 3(x + 9) ÷ 7 = 9 for x.

    12

    Multiply both sides by 7 to get 3(x + 9) = 63. Divide by 3 to get x + 9 = 21, so x = 12.

  2. 2. Solve the algebraic fraction equation 6(x + 38) ÷ 3 = 84 for x.

    4

    Multiply both sides by 3 to get 6(x + 38) = 252. Divide by 6 to get x + 38 = 42, so x = 4.

  3. 3. Solve the algebraic fraction equation 5(x + 38) ÷ 5 = 65 for x.

    27

    Multiply both sides by 5 to get 5(x + 38) = 325. Divide by 5 to get x + 38 = 65, so x = 27.

  4. 4. Solve the algebraic fraction equation 5(x + 12) ÷ 5 = 25 for x.

    13

    Multiply both sides by 5 to get 5(x + 12) = 125. Divide by 5 to get x + 12 = 25, so x = 13.

  5. 5. Solve the algebraic fraction equation 5(x + 9) ÷ 5 = 50 for x.

    41

    Multiply both sides by 5 to get 5(x + 9) = 250. Divide by 5 to get x + 9 = 50, so x = 41.

  6. 6. Solve the algebraic fraction equation 6(x + 3) ÷ 2 = 18 for x.

    3

    Multiply both sides by 2 to get 6(x + 3) = 36. Divide by 6 to get x + 3 = 6, so x = 3.

  7. 7. Solve the algebraic fraction equation 4(x + 17) ÷ 2 = 44 for x.

    5

    Multiply both sides by 2 to get 4(x + 17) = 88. Divide by 4 to get x + 17 = 22, so x = 5.

  8. 8. Solve the algebraic fraction equation 6(x + 9) ÷ 2 = 78 for x.

    17

    Multiply both sides by 2 to get 6(x + 9) = 156. Divide by 6 to get x + 9 = 26, so x = 17.

  9. 9. Solve the algebraic fraction equation 2(x + 5) ÷ 7 = 18 for x.

    58

    Multiply both sides by 7 to get 2(x + 5) = 126. Divide by 2 to get x + 5 = 63, so x = 58.

  10. 10. Solve the algebraic fraction equation 4(x + 10) ÷ 4 = 32 for x.

    22

    Multiply both sides by 4 to get 4(x + 10) = 128. Divide by 4 to get x + 10 = 32, so x = 22.

  11. 11. Solve the algebraic fraction equation 4(x + 1) ÷ 2 = 16 for x.

    7

    Multiply both sides by 2 to get 4(x + 1) = 32. Divide by 4 to get x + 1 = 8, so x = 7.

  12. 12. Solve the algebraic fraction equation 4(x + 57) ÷ 6 = 44 for x.

    9

    Multiply both sides by 6 to get 4(x + 57) = 264. Divide by 4 to get x + 57 = 66, so x = 9.

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