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 + 29) ÷ 6 = 36 for x.
LHS = RHS 4(x + 29) ÷ 6 = 36 · x + 29 = 54 → x = ?
2. Solve the algebraic fraction equation 2(x + 22) ÷ 4 = 26 for x.
LHS = RHS 2(x + 22) ÷ 4 = 26 · x + 22 = 52 → x = ?
3. Solve the algebraic fraction equation 5(x + 5) ÷ 2 = 20 for x.
LHS = RHS 5(x + 5) ÷ 2 = 20 · x + 5 = 8 → x = ?
4. Solve the algebraic fraction equation 5(x + 2) ÷ 5 = 25 for x.
LHS = RHS 5(x + 2) ÷ 5 = 25 · x + 2 = 25 → x = ?
5. Solve the algebraic fraction equation 4(x + 7) ÷ 4 = 32 for x.
LHS = RHS 4(x + 7) ÷ 4 = 32 · x + 7 = 32 → x = ?
6. Solve the algebraic fraction equation 6(x + 19) ÷ 7 = 78 for x.
LHS = RHS 6(x + 19) ÷ 7 = 78 · x + 19 = 91 → x = ?
7. Solve the algebraic fraction equation 3(x + 21) ÷ 7 = 39 for x.
LHS = RHS 3(x + 21) ÷ 7 = 39 · x + 21 = 91 → x = ?
8. Solve the algebraic fraction equation 2(x + 33) ÷ 7 = 18 for x.
LHS = RHS 2(x + 33) ÷ 7 = 18 · x + 33 = 63 → x = ?
9. Solve the algebraic fraction equation 5(x + 13) ÷ 5 = 20 for x.
LHS = RHS 5(x + 13) ÷ 5 = 20 · x + 13 = 20 → x = ?
10. Solve the algebraic fraction equation 2(x + 25) ÷ 5 = 16 for x.
LHS = RHS 2(x + 25) ÷ 5 = 16 · x + 25 = 40 → x = ?
11. Solve the algebraic fraction equation 4(x + 25) ÷ 7 = 20 for x.
LHS = RHS 4(x + 25) ÷ 7 = 20 · x + 25 = 35 → x = ?
12. Solve the algebraic fraction equation 5(x + 2) ÷ 2 = 10 for x.
LHS = RHS 5(x + 2) ÷ 2 = 10 · x + 2 = 4 → x = ?
12 questions · Seed 104729 · 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 + 29) ÷ 6 = 36 for x.
25 Multiply both sides by 6 to get 4(x + 29) = 216. Divide by 4 to get x + 29 = 54, so x = 25.
2. Solve the algebraic fraction equation 2(x + 22) ÷ 4 = 26 for x.
30 Multiply both sides by 4 to get 2(x + 22) = 104. Divide by 2 to get x + 22 = 52, so x = 30.
3. Solve the algebraic fraction equation 5(x + 5) ÷ 2 = 20 for x.
3 Multiply both sides by 2 to get 5(x + 5) = 40. Divide by 5 to get x + 5 = 8, so x = 3.
4. Solve the algebraic fraction equation 5(x + 2) ÷ 5 = 25 for x.
23 Multiply both sides by 5 to get 5(x + 2) = 125. Divide by 5 to get x + 2 = 25, so x = 23.
5. Solve the algebraic fraction equation 4(x + 7) ÷ 4 = 32 for x.
25 Multiply both sides by 4 to get 4(x + 7) = 128. Divide by 4 to get x + 7 = 32, so x = 25.
6. Solve the algebraic fraction equation 6(x + 19) ÷ 7 = 78 for x.
72 Multiply both sides by 7 to get 6(x + 19) = 546. Divide by 6 to get x + 19 = 91, so x = 72.
7. Solve the algebraic fraction equation 3(x + 21) ÷ 7 = 39 for x.
70 Multiply both sides by 7 to get 3(x + 21) = 273. Divide by 3 to get x + 21 = 91, so x = 70.
8. Solve the algebraic fraction equation 2(x + 33) ÷ 7 = 18 for x.
30 Multiply both sides by 7 to get 2(x + 33) = 126. Divide by 2 to get x + 33 = 63, so x = 30.
9. Solve the algebraic fraction equation 5(x + 13) ÷ 5 = 20 for x.
7 Multiply both sides by 5 to get 5(x + 13) = 100. Divide by 5 to get x + 13 = 20, so x = 7.
10. Solve the algebraic fraction equation 2(x + 25) ÷ 5 = 16 for x.
15 Multiply both sides by 5 to get 2(x + 25) = 80. Divide by 2 to get x + 25 = 40, so x = 15.
11. Solve the algebraic fraction equation 4(x + 25) ÷ 7 = 20 for x.
10 Multiply both sides by 7 to get 4(x + 25) = 140. Divide by 4 to get x + 25 = 35, so x = 10.
12. Solve the algebraic fraction equation 5(x + 2) ÷ 2 = 10 for x.
2 Multiply both sides by 2 to get 5(x + 2) = 20. Divide by 5 to get x + 2 = 4, so x = 2.
12 questions · Seed 104729 · 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 + 29) ÷ 6 = 36 for x.
LHS = RHS 4(x + 29) ÷ 6 = 36 · x + 29 = 54 → x = ?
2. Solve the algebraic fraction equation 2(x + 22) ÷ 4 = 26 for x.
LHS = RHS 2(x + 22) ÷ 4 = 26 · x + 22 = 52 → x = ?
3. Solve the algebraic fraction equation 5(x + 5) ÷ 2 = 20 for x.
LHS = RHS 5(x + 5) ÷ 2 = 20 · x + 5 = 8 → x = ?
4. Solve the algebraic fraction equation 5(x + 2) ÷ 5 = 25 for x.
LHS = RHS 5(x + 2) ÷ 5 = 25 · x + 2 = 25 → x = ?
5. Solve the algebraic fraction equation 4(x + 7) ÷ 4 = 32 for x.
LHS = RHS 4(x + 7) ÷ 4 = 32 · x + 7 = 32 → x = ?
6. Solve the algebraic fraction equation 6(x + 19) ÷ 7 = 78 for x.
LHS = RHS 6(x + 19) ÷ 7 = 78 · x + 19 = 91 → x = ?
7. Solve the algebraic fraction equation 3(x + 21) ÷ 7 = 39 for x.
LHS = RHS 3(x + 21) ÷ 7 = 39 · x + 21 = 91 → x = ?
8. Solve the algebraic fraction equation 2(x + 33) ÷ 7 = 18 for x.
LHS = RHS 2(x + 33) ÷ 7 = 18 · x + 33 = 63 → x = ?
9. Solve the algebraic fraction equation 5(x + 13) ÷ 5 = 20 for x.
LHS = RHS 5(x + 13) ÷ 5 = 20 · x + 13 = 20 → x = ?
10. Solve the algebraic fraction equation 2(x + 25) ÷ 5 = 16 for x.
LHS = RHS 2(x + 25) ÷ 5 = 16 · x + 25 = 40 → x = ?
11. Solve the algebraic fraction equation 4(x + 25) ÷ 7 = 20 for x.
LHS = RHS 4(x + 25) ÷ 7 = 20 · x + 25 = 35 → x = ?
12. Solve the algebraic fraction equation 5(x + 2) ÷ 2 = 10 for x.
LHS = RHS 5(x + 2) ÷ 2 = 10 · x + 2 = 4 → x = ?
12 questions · Seed 104729 · 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 + 29) ÷ 6 = 36 for x.
25 Multiply both sides by 6 to get 4(x + 29) = 216. Divide by 4 to get x + 29 = 54, so x = 25.
2. Solve the algebraic fraction equation 2(x + 22) ÷ 4 = 26 for x.
30 Multiply both sides by 4 to get 2(x + 22) = 104. Divide by 2 to get x + 22 = 52, so x = 30.
3. Solve the algebraic fraction equation 5(x + 5) ÷ 2 = 20 for x.
3 Multiply both sides by 2 to get 5(x + 5) = 40. Divide by 5 to get x + 5 = 8, so x = 3.
4. Solve the algebraic fraction equation 5(x + 2) ÷ 5 = 25 for x.
23 Multiply both sides by 5 to get 5(x + 2) = 125. Divide by 5 to get x + 2 = 25, so x = 23.
5. Solve the algebraic fraction equation 4(x + 7) ÷ 4 = 32 for x.
25 Multiply both sides by 4 to get 4(x + 7) = 128. Divide by 4 to get x + 7 = 32, so x = 25.
6. Solve the algebraic fraction equation 6(x + 19) ÷ 7 = 78 for x.
72 Multiply both sides by 7 to get 6(x + 19) = 546. Divide by 6 to get x + 19 = 91, so x = 72.
7. Solve the algebraic fraction equation 3(x + 21) ÷ 7 = 39 for x.
70 Multiply both sides by 7 to get 3(x + 21) = 273. Divide by 3 to get x + 21 = 91, so x = 70.
8. Solve the algebraic fraction equation 2(x + 33) ÷ 7 = 18 for x.
30 Multiply both sides by 7 to get 2(x + 33) = 126. Divide by 2 to get x + 33 = 63, so x = 30.
9. Solve the algebraic fraction equation 5(x + 13) ÷ 5 = 20 for x.
7 Multiply both sides by 5 to get 5(x + 13) = 100. Divide by 5 to get x + 13 = 20, so x = 7.
10. Solve the algebraic fraction equation 2(x + 25) ÷ 5 = 16 for x.
15 Multiply both sides by 5 to get 2(x + 25) = 80. Divide by 2 to get x + 25 = 40, so x = 15.
11. Solve the algebraic fraction equation 4(x + 25) ÷ 7 = 20 for x.
10 Multiply both sides by 7 to get 4(x + 25) = 140. Divide by 4 to get x + 25 = 35, so x = 10.
12. Solve the algebraic fraction equation 5(x + 2) ÷ 2 = 10 for x.
2 Multiply both sides by 2 to get 5(x + 2) = 20. Divide by 5 to get x + 2 = 4, so x = 2.
12 questions · Seed 104729 · Age guidance, not curriculum certification
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