Back to worksheets Maths Ages 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.
Student worksheet Answer key
Worksheet Studio Practice pack · Ages 13-15
Equations with brackets & fractions Take your time. Show your thinking.
1. Solve the algebraic fraction equation 4(x + 24) ÷ 5 = 56 for x.
LHS = RHS 4(x + 24) ÷ 5 = 56 · x + 24 = 70 → x = ?
2. Solve the algebraic fraction equation 5(x + 9) ÷ 7 = 65 for x.
LHS = RHS 5(x + 9) ÷ 7 = 65 · x + 9 = 91 → x = ?
3. Solve the algebraic fraction equation 3(x + 26) ÷ 6 = 15 for x.
LHS = RHS 3(x + 26) ÷ 6 = 15 · x + 26 = 30 → x = ?
4. Solve the algebraic fraction equation 5(x + 27) ÷ 5 = 55 for x.
LHS = RHS 5(x + 27) ÷ 5 = 55 · x + 27 = 55 → x = ?
5. Solve the algebraic fraction equation 4(x + 2) ÷ 2 = 8 for x.
LHS = RHS 4(x + 2) ÷ 2 = 8 · x + 2 = 4 → x = ?
6. Solve the algebraic fraction equation 2(x + 5) ÷ 4 = 10 for x.
LHS = RHS 2(x + 5) ÷ 4 = 10 · x + 5 = 20 → x = ?
7. Solve the algebraic fraction equation 5(x + 5) ÷ 6 = 20 for x.
LHS = RHS 5(x + 5) ÷ 6 = 20 · x + 5 = 24 → x = ?
8. Solve the algebraic fraction equation 3(x + 37) ÷ 7 = 24 for x.
LHS = RHS 3(x + 37) ÷ 7 = 24 · x + 37 = 56 → x = ?
9. Solve the algebraic fraction equation 4(x + 2) ÷ 3 = 8 for x.
LHS = RHS 4(x + 2) ÷ 3 = 8 · x + 2 = 6 → x = ?
10. Solve the algebraic fraction equation 6(x + 18) ÷ 5 = 66 for x.
LHS = RHS 6(x + 18) ÷ 5 = 66 · x + 18 = 55 → x = ?
11. Solve the algebraic fraction equation 3(x + 1) ÷ 2 = 6 for x.
LHS = RHS 3(x + 1) ÷ 2 = 6 · x + 1 = 4 → x = ?
12. Solve the algebraic fraction equation 5(x + 22) ÷ 3 = 60 for x.
LHS = RHS 5(x + 22) ÷ 3 = 60 · x + 22 = 36 → x = ?
12 questions · Seed 44 · Age guidance, not curriculum certification
View the answer key Worksheet Studio Answer key · Ages 13-15
Equations with brackets & fractions Answers and reasoning. Review before teaching.
1. Solve the algebraic fraction equation 4(x + 24) ÷ 5 = 56 for x.
46 Multiply both sides by 5 to get 4(x + 24) = 280. Divide by 4 to get x + 24 = 70, so x = 46.
2. Solve the algebraic fraction equation 5(x + 9) ÷ 7 = 65 for x.
82 Multiply both sides by 7 to get 5(x + 9) = 455. Divide by 5 to get x + 9 = 91, so x = 82.
3. Solve the algebraic fraction equation 3(x + 26) ÷ 6 = 15 for x.
4 Multiply both sides by 6 to get 3(x + 26) = 90. Divide by 3 to get x + 26 = 30, so x = 4.
4. Solve the algebraic fraction equation 5(x + 27) ÷ 5 = 55 for x.
28 Multiply both sides by 5 to get 5(x + 27) = 275. Divide by 5 to get x + 27 = 55, so x = 28.
5. Solve the algebraic fraction equation 4(x + 2) ÷ 2 = 8 for x.
2 Multiply both sides by 2 to get 4(x + 2) = 16. Divide by 4 to get x + 2 = 4, so x = 2.
6. Solve the algebraic fraction equation 2(x + 5) ÷ 4 = 10 for x.
15 Multiply both sides by 4 to get 2(x + 5) = 40. Divide by 2 to get x + 5 = 20, so x = 15.
7. Solve the algebraic fraction equation 5(x + 5) ÷ 6 = 20 for x.
19 Multiply both sides by 6 to get 5(x + 5) = 120. Divide by 5 to get x + 5 = 24, so x = 19.
8. Solve the algebraic fraction equation 3(x + 37) ÷ 7 = 24 for x.
19 Multiply both sides by 7 to get 3(x + 37) = 168. Divide by 3 to get x + 37 = 56, so x = 19.
9. Solve the algebraic fraction equation 4(x + 2) ÷ 3 = 8 for x.
4 Multiply both sides by 3 to get 4(x + 2) = 24. Divide by 4 to get x + 2 = 6, so x = 4.
10. Solve the algebraic fraction equation 6(x + 18) ÷ 5 = 66 for x.
37 Multiply both sides by 5 to get 6(x + 18) = 330. Divide by 6 to get x + 18 = 55, so x = 37.
11. Solve the algebraic fraction equation 3(x + 1) ÷ 2 = 6 for x.
3 Multiply both sides by 2 to get 3(x + 1) = 12. Divide by 3 to get x + 1 = 4, so x = 3.
12. Solve the algebraic fraction equation 5(x + 22) ÷ 3 = 60 for x.
14 Multiply both sides by 3 to get 5(x + 22) = 180. Divide by 5 to get x + 22 = 36, so x = 14.
12 questions · Seed 44 · Age guidance, not curriculum certification
Worksheet Studio Practice pack · Ages 13-15
Equations with brackets & fractions Take your time. Show your thinking.
1. Solve the algebraic fraction equation 4(x + 24) ÷ 5 = 56 for x.
LHS = RHS 4(x + 24) ÷ 5 = 56 · x + 24 = 70 → x = ?
2. Solve the algebraic fraction equation 5(x + 9) ÷ 7 = 65 for x.
LHS = RHS 5(x + 9) ÷ 7 = 65 · x + 9 = 91 → x = ?
3. Solve the algebraic fraction equation 3(x + 26) ÷ 6 = 15 for x.
LHS = RHS 3(x + 26) ÷ 6 = 15 · x + 26 = 30 → x = ?
4. Solve the algebraic fraction equation 5(x + 27) ÷ 5 = 55 for x.
LHS = RHS 5(x + 27) ÷ 5 = 55 · x + 27 = 55 → x = ?
5. Solve the algebraic fraction equation 4(x + 2) ÷ 2 = 8 for x.
LHS = RHS 4(x + 2) ÷ 2 = 8 · x + 2 = 4 → x = ?
6. Solve the algebraic fraction equation 2(x + 5) ÷ 4 = 10 for x.
LHS = RHS 2(x + 5) ÷ 4 = 10 · x + 5 = 20 → x = ?
7. Solve the algebraic fraction equation 5(x + 5) ÷ 6 = 20 for x.
LHS = RHS 5(x + 5) ÷ 6 = 20 · x + 5 = 24 → x = ?
8. Solve the algebraic fraction equation 3(x + 37) ÷ 7 = 24 for x.
LHS = RHS 3(x + 37) ÷ 7 = 24 · x + 37 = 56 → x = ?
9. Solve the algebraic fraction equation 4(x + 2) ÷ 3 = 8 for x.
LHS = RHS 4(x + 2) ÷ 3 = 8 · x + 2 = 6 → x = ?
10. Solve the algebraic fraction equation 6(x + 18) ÷ 5 = 66 for x.
LHS = RHS 6(x + 18) ÷ 5 = 66 · x + 18 = 55 → x = ?
11. Solve the algebraic fraction equation 3(x + 1) ÷ 2 = 6 for x.
LHS = RHS 3(x + 1) ÷ 2 = 6 · x + 1 = 4 → x = ?
12. Solve the algebraic fraction equation 5(x + 22) ÷ 3 = 60 for x.
LHS = RHS 5(x + 22) ÷ 3 = 60 · x + 22 = 36 → x = ?
12 questions · Seed 44 · Age guidance, not curriculum certification
Worksheet Studio Answer key · Ages 13-15
Equations with brackets & fractions Answers and reasoning. Review before teaching.
1. Solve the algebraic fraction equation 4(x + 24) ÷ 5 = 56 for x.
46 Multiply both sides by 5 to get 4(x + 24) = 280. Divide by 4 to get x + 24 = 70, so x = 46.
2. Solve the algebraic fraction equation 5(x + 9) ÷ 7 = 65 for x.
82 Multiply both sides by 7 to get 5(x + 9) = 455. Divide by 5 to get x + 9 = 91, so x = 82.
3. Solve the algebraic fraction equation 3(x + 26) ÷ 6 = 15 for x.
4 Multiply both sides by 6 to get 3(x + 26) = 90. Divide by 3 to get x + 26 = 30, so x = 4.
4. Solve the algebraic fraction equation 5(x + 27) ÷ 5 = 55 for x.
28 Multiply both sides by 5 to get 5(x + 27) = 275. Divide by 5 to get x + 27 = 55, so x = 28.
5. Solve the algebraic fraction equation 4(x + 2) ÷ 2 = 8 for x.
2 Multiply both sides by 2 to get 4(x + 2) = 16. Divide by 4 to get x + 2 = 4, so x = 2.
6. Solve the algebraic fraction equation 2(x + 5) ÷ 4 = 10 for x.
15 Multiply both sides by 4 to get 2(x + 5) = 40. Divide by 2 to get x + 5 = 20, so x = 15.
7. Solve the algebraic fraction equation 5(x + 5) ÷ 6 = 20 for x.
19 Multiply both sides by 6 to get 5(x + 5) = 120. Divide by 5 to get x + 5 = 24, so x = 19.
8. Solve the algebraic fraction equation 3(x + 37) ÷ 7 = 24 for x.
19 Multiply both sides by 7 to get 3(x + 37) = 168. Divide by 3 to get x + 37 = 56, so x = 19.
9. Solve the algebraic fraction equation 4(x + 2) ÷ 3 = 8 for x.
4 Multiply both sides by 3 to get 4(x + 2) = 24. Divide by 4 to get x + 2 = 6, so x = 4.
10. Solve the algebraic fraction equation 6(x + 18) ÷ 5 = 66 for x.
37 Multiply both sides by 5 to get 6(x + 18) = 330. Divide by 6 to get x + 18 = 55, so x = 37.
11. Solve the algebraic fraction equation 3(x + 1) ÷ 2 = 6 for x.
3 Multiply both sides by 2 to get 3(x + 1) = 12. Divide by 3 to get x + 1 = 4, so x = 3.
12. Solve the algebraic fraction equation 5(x + 22) ÷ 3 = 60 for x.
14 Multiply both sides by 3 to get 5(x + 22) = 180. Divide by 5 to get x + 22 = 36, so x = 14.
12 questions · Seed 44 · Age guidance, not curriculum certification
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