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 5(x + 38) ÷ 5 = 40 for x.
LHS = RHS 5(x + 38) ÷ 5 = 40 · x + 38 = 40 → x = ?
2. Solve the algebraic fraction equation 6(x + 19) ÷ 7 = 54 for x.
LHS = RHS 6(x + 19) ÷ 7 = 54 · x + 19 = 63 → x = ?
3. Solve the algebraic fraction equation 4(x + 8) ÷ 6 = 56 for x.
LHS = RHS 4(x + 8) ÷ 6 = 56 · x + 8 = 84 → x = ?
4. Solve the algebraic fraction equation 4(x + 10) ÷ 6 = 24 for x.
LHS = RHS 4(x + 10) ÷ 6 = 24 · x + 10 = 36 → x = ?
5. Solve the algebraic fraction equation 4(x + 53) ÷ 4 = 56 for x.
LHS = RHS 4(x + 53) ÷ 4 = 56 · x + 53 = 56 → x = ?
6. Solve the algebraic fraction equation 2(x + 20) ÷ 6 = 12 for x.
LHS = RHS 2(x + 20) ÷ 6 = 12 · x + 20 = 36 → x = ?
7. Solve the algebraic fraction equation 3(x + 39) ÷ 6 = 30 for x.
LHS = RHS 3(x + 39) ÷ 6 = 30 · x + 39 = 60 → x = ?
8. Solve the algebraic fraction equation 4(x + 6) ÷ 7 = 32 for x.
LHS = RHS 4(x + 6) ÷ 7 = 32 · x + 6 = 56 → x = ?
9. Solve the algebraic fraction equation 4(x + 12) ÷ 3 = 24 for x.
LHS = RHS 4(x + 12) ÷ 3 = 24 · x + 12 = 18 → x = ?
10. Solve the algebraic fraction equation 6(x + 8) ÷ 4 = 36 for x.
LHS = RHS 6(x + 8) ÷ 4 = 36 · x + 8 = 24 → x = ?
11. Solve the algebraic fraction equation 4(x + 3) ÷ 2 = 56 for x.
LHS = RHS 4(x + 3) ÷ 2 = 56 · x + 3 = 28 → x = ?
12. Solve the algebraic fraction equation 6(x + 9) ÷ 4 = 60 for x.
LHS = RHS 6(x + 9) ÷ 4 = 60 · x + 9 = 40 → x = ?
12 questions · Seed 42 · 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 5(x + 38) ÷ 5 = 40 for x.
2 Multiply both sides by 5 to get 5(x + 38) = 200. Divide by 5 to get x + 38 = 40, so x = 2.
2. Solve the algebraic fraction equation 6(x + 19) ÷ 7 = 54 for x.
44 Multiply both sides by 7 to get 6(x + 19) = 378. Divide by 6 to get x + 19 = 63, so x = 44.
3. Solve the algebraic fraction equation 4(x + 8) ÷ 6 = 56 for x.
76 Multiply both sides by 6 to get 4(x + 8) = 336. Divide by 4 to get x + 8 = 84, so x = 76.
4. Solve the algebraic fraction equation 4(x + 10) ÷ 6 = 24 for x.
26 Multiply both sides by 6 to get 4(x + 10) = 144. Divide by 4 to get x + 10 = 36, so x = 26.
5. Solve the algebraic fraction equation 4(x + 53) ÷ 4 = 56 for x.
3 Multiply both sides by 4 to get 4(x + 53) = 224. Divide by 4 to get x + 53 = 56, so x = 3.
6. Solve the algebraic fraction equation 2(x + 20) ÷ 6 = 12 for x.
16 Multiply both sides by 6 to get 2(x + 20) = 72. Divide by 2 to get x + 20 = 36, so x = 16.
7. Solve the algebraic fraction equation 3(x + 39) ÷ 6 = 30 for x.
21 Multiply both sides by 6 to get 3(x + 39) = 180. Divide by 3 to get x + 39 = 60, so x = 21.
8. Solve the algebraic fraction equation 4(x + 6) ÷ 7 = 32 for x.
50 Multiply both sides by 7 to get 4(x + 6) = 224. Divide by 4 to get x + 6 = 56, so x = 50.
9. Solve the algebraic fraction equation 4(x + 12) ÷ 3 = 24 for x.
6 Multiply both sides by 3 to get 4(x + 12) = 72. Divide by 4 to get x + 12 = 18, so x = 6.
10. Solve the algebraic fraction equation 6(x + 8) ÷ 4 = 36 for x.
16 Multiply both sides by 4 to get 6(x + 8) = 144. Divide by 6 to get x + 8 = 24, so x = 16.
11. Solve the algebraic fraction equation 4(x + 3) ÷ 2 = 56 for x.
25 Multiply both sides by 2 to get 4(x + 3) = 112. Divide by 4 to get x + 3 = 28, so x = 25.
12. Solve the algebraic fraction equation 6(x + 9) ÷ 4 = 60 for x.
31 Multiply both sides by 4 to get 6(x + 9) = 240. Divide by 6 to get x + 9 = 40, so x = 31.
12 questions · Seed 42 · 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 5(x + 38) ÷ 5 = 40 for x.
LHS = RHS 5(x + 38) ÷ 5 = 40 · x + 38 = 40 → x = ?
2. Solve the algebraic fraction equation 6(x + 19) ÷ 7 = 54 for x.
LHS = RHS 6(x + 19) ÷ 7 = 54 · x + 19 = 63 → x = ?
3. Solve the algebraic fraction equation 4(x + 8) ÷ 6 = 56 for x.
LHS = RHS 4(x + 8) ÷ 6 = 56 · x + 8 = 84 → x = ?
4. Solve the algebraic fraction equation 4(x + 10) ÷ 6 = 24 for x.
LHS = RHS 4(x + 10) ÷ 6 = 24 · x + 10 = 36 → x = ?
5. Solve the algebraic fraction equation 4(x + 53) ÷ 4 = 56 for x.
LHS = RHS 4(x + 53) ÷ 4 = 56 · x + 53 = 56 → x = ?
6. Solve the algebraic fraction equation 2(x + 20) ÷ 6 = 12 for x.
LHS = RHS 2(x + 20) ÷ 6 = 12 · x + 20 = 36 → x = ?
7. Solve the algebraic fraction equation 3(x + 39) ÷ 6 = 30 for x.
LHS = RHS 3(x + 39) ÷ 6 = 30 · x + 39 = 60 → x = ?
8. Solve the algebraic fraction equation 4(x + 6) ÷ 7 = 32 for x.
LHS = RHS 4(x + 6) ÷ 7 = 32 · x + 6 = 56 → x = ?
9. Solve the algebraic fraction equation 4(x + 12) ÷ 3 = 24 for x.
LHS = RHS 4(x + 12) ÷ 3 = 24 · x + 12 = 18 → x = ?
10. Solve the algebraic fraction equation 6(x + 8) ÷ 4 = 36 for x.
LHS = RHS 6(x + 8) ÷ 4 = 36 · x + 8 = 24 → x = ?
11. Solve the algebraic fraction equation 4(x + 3) ÷ 2 = 56 for x.
LHS = RHS 4(x + 3) ÷ 2 = 56 · x + 3 = 28 → x = ?
12. Solve the algebraic fraction equation 6(x + 9) ÷ 4 = 60 for x.
LHS = RHS 6(x + 9) ÷ 4 = 60 · x + 9 = 40 → x = ?
12 questions · Seed 42 · 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 5(x + 38) ÷ 5 = 40 for x.
2 Multiply both sides by 5 to get 5(x + 38) = 200. Divide by 5 to get x + 38 = 40, so x = 2.
2. Solve the algebraic fraction equation 6(x + 19) ÷ 7 = 54 for x.
44 Multiply both sides by 7 to get 6(x + 19) = 378. Divide by 6 to get x + 19 = 63, so x = 44.
3. Solve the algebraic fraction equation 4(x + 8) ÷ 6 = 56 for x.
76 Multiply both sides by 6 to get 4(x + 8) = 336. Divide by 4 to get x + 8 = 84, so x = 76.
4. Solve the algebraic fraction equation 4(x + 10) ÷ 6 = 24 for x.
26 Multiply both sides by 6 to get 4(x + 10) = 144. Divide by 4 to get x + 10 = 36, so x = 26.
5. Solve the algebraic fraction equation 4(x + 53) ÷ 4 = 56 for x.
3 Multiply both sides by 4 to get 4(x + 53) = 224. Divide by 4 to get x + 53 = 56, so x = 3.
6. Solve the algebraic fraction equation 2(x + 20) ÷ 6 = 12 for x.
16 Multiply both sides by 6 to get 2(x + 20) = 72. Divide by 2 to get x + 20 = 36, so x = 16.
7. Solve the algebraic fraction equation 3(x + 39) ÷ 6 = 30 for x.
21 Multiply both sides by 6 to get 3(x + 39) = 180. Divide by 3 to get x + 39 = 60, so x = 21.
8. Solve the algebraic fraction equation 4(x + 6) ÷ 7 = 32 for x.
50 Multiply both sides by 7 to get 4(x + 6) = 224. Divide by 4 to get x + 6 = 56, so x = 50.
9. Solve the algebraic fraction equation 4(x + 12) ÷ 3 = 24 for x.
6 Multiply both sides by 3 to get 4(x + 12) = 72. Divide by 4 to get x + 12 = 18, so x = 6.
10. Solve the algebraic fraction equation 6(x + 8) ÷ 4 = 36 for x.
16 Multiply both sides by 4 to get 6(x + 8) = 144. Divide by 6 to get x + 8 = 24, so x = 16.
11. Solve the algebraic fraction equation 4(x + 3) ÷ 2 = 56 for x.
25 Multiply both sides by 2 to get 4(x + 3) = 112. Divide by 4 to get x + 3 = 28, so x = 25.
12. Solve the algebraic fraction equation 6(x + 9) ÷ 4 = 60 for x.
31 Multiply both sides by 4 to get 6(x + 9) = 240. Divide by 6 to get x + 9 = 40, so x = 31.
12 questions · Seed 42 · Age guidance, not curriculum certification
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