Two-step Equations Worksheet Answer Key – Grade 7

Problem 1 Add, Then Multiply

Subtract 5: 3x = 24. Divide by 3: x = 8. Check: 3(8) + 5 = 29.

x = 8

Problem 2 Subtract, Then Multiply

Add 4: 5x = 35. Divide by 5: x = 7. Check: 5(7) − 4 = 31.

x = 7

Problem 3 A Quotient Plus a Constant

Subtract 3: x4 = 6. Multiply by 4: x = 24. Check: 24 ÷ 4 + 3 = 9.

x = 24

Problem 4 Read the Tape Diagram

The two equal parts together are 31 − 9 = 22, so each part is 22 ÷ 2 = 11. Algebra: 2x = 22 and x = 11.

x = 11

Problem 5 A Negative Coefficient

Subtract 6: −4x = 24. Divide by −4: x = −6. Check: −4(−6) + 6 = 24 + 6 = 30.

x = −6

Problem 6 Decimal Coefficient

Add 3.5: 2.5x = 15. Divide by 2.5: x = 6. Check: 2.5(6) − 3.5 = 15 − 3.5 = 11.5.

x = 6

Problem 7 Fraction Coefficient

Subtract 5: 78x = 14. Multiply by 87: x = 16. Check: 78(16) + 5 = 14 + 5 = 19.

x = 16

Problem 8 Two Ways with Parentheses

Divide first: x + 3 = 9, so x = 6.

Distribute first: 4x + 12 = 36, so 4x = 24 and x = 6.

x = 6 by both methods.

Problem 9 Negative Factor Outside

Divide by −2: x − 5 = −9. Add 5: x = −4. Check: −2(−4 − 5) = −2(−9) = 18.

x = −4

Problem 10 Decimal Factor Outside

Divide by 0.4: x − 3 = 7. Add 3: x = 10. Check: 0.4(7) = 2.8.

x = 10

Problem 11 Negative Quotient

Add 4: −x3 = 6. Multiply by −3: x = −18. Check: −(−18) ÷ 3 − 4 = 6 − 4 = 2.

x = −18

Problem 12 Variable on the Right

Subtract 2.6: 1.3x = −7.8. Divide by 1.3: x = −6. Check: 2.6 + 1.3(−6) = 2.6 − 7.8 = −5.2.

x = −6

Problem 13 Fractions Inside and Out

Multiply by 32: x + 34 = 154. Subtract 34: x = 124 = 3. Check: 23 · 154 = 3012 = 52.

x = 3

Problem 14 Arithmetic and Algebra

Arithmetic: add 3.5 to get 24, then divide by 6 to get 4.

Algebra: 6x − 3.5 = 20.5, so 6x = 24 and x = 4.

The number is 4

Problem 15 Summer Camp Cost

Let w = weeks: 85w + 60 = 485. Estimate: 485 − 60 ≈ 425, and 425 ÷ 85 is 5.

Solve: 85w = 425, so w = 5. Check: 85(5) + 60 = 485.

5 weeks

Problem 16 Hours at the Food Truck

9.75h + 30 = 108. Subtract 30: 9.75h = 78. Divide: h = 8. Check: 9.75(8) = 78 and 78 + 30 = 108.

8 hours

Problem 17 Fencing a Rectangle

Perimeter = 2(x + 6.5) = 31. Divide by 2: x + 6.5 = 15.5. Subtract: x = 9.

Check: 2(9 + 6.5) = 2(15.5) = 31.

9 feet

Problem 18 Fahrenheit and Celsius

77 = 1.8C + 32. Subtract 32: 45 = 1.8C. Divide by 1.8: C = 25. Check: 1.8(25) + 32 = 45 + 32 = 77.

25°C

Problem 19 Group Tickets with a Fee

Each ticket with fee costs about 87 ÷ 6 ≈ 14.5, so t is about 12.

6(t + 2.5) = 87. Divide by 6: t + 2.5 = 14.5. Subtract: t = 12. Check: 6(14.5) = 87.

$12 per ticket

Problem 20 Descending the Trail

1,240 − 36m = 340. Subtract 1,240: −36m = −900. Divide by −36: m = 25.

Check: 1,240 − 36(25) = 1,240 − 900 = 340.

25 minutes of descent bring the hiker to 340 feet.