Worksheet for solving equations using the distributive property, including ten algebra problems.

I'll solve each equation step by step using the distributive property.

Problem 1: 5(4x + 8) = 80
- Distribute: 20x + 40 = 80
- Subtract 40 from both sides: 20x = 40
- Divide by 20: x = 2

Problem 2: -4x = 3(x + 7)
- Distribute on right side: -4x = 3x + 21
- Subtract 3x from both sides: -7x = 21
- Divide by -7: x = -3

Problem 3: 2(x - 1) + 3x = 3
- Distribute: 2x - 2 + 3x = 3
- Combine like terms: 5x - 2 = 3
- Add 2 to both sides: 5x = 5
- Divide by 5: x = 1

Problem 4: (3/2)(3x + 5) = -24
- Distribute: (9x/2) + (15/2) = -24
- Multiply both sides by 2: 9x + 15 = -48
- Subtract 15 from both sides: 9x = -63
- Divide by 9: x = -7

Problem 5: 3(x - 2) = 18
- Distribute: 3x - 6 = 18
- Add 6 to both sides: 3x = 24
- Divide by 3: x = 8

Problem 6: 0.25(3 + x) = 0.5
- Distribute: 0.75 + 0.25x = 0.5
- Subtract 0.75 from both sides: 0.25x = -0.25
- Divide by 0.25: x = -1

Problem 7: 2(3x - 1) + 2(4x + 5) = 16
- Distribute both parts: 6x - 2 + 8x + 10 = 16
- Combine like terms: 14x + 8 = 16
- Subtract 8 from both sides: 14x = 8
- Divide by 14: x = 8/14 = 4/7

Problem 8: -2 - 3(1 - 4x) = -53
- Distribute: -2 - 3 + 12x = -53
- Combine constants: -5 + 12x = -53
- Add 5 to both sides: 12x = -48
- Divide by 12: x = -4

Problem 9: -111 = 3(7x - 2)
- Distribute: -111 = 21x - 6
- Add 6 to both sides: -105 = 21x
- Divide by 21: x = -5

Problem 10: -86 = 4 + 5(3x - 3)
- Distribute: -86 = 4 + 15x - 15
- Combine constants on right: -86 = 15x - 11
- Add 11 to both sides: -75 = 15x
- Divide by 15: x = -5

Let me verify my calculations once more before providing the final answer...

All calculations check out correctly.

Final Answer:
1) x = 2
2) x = -3
3) x = 1
4) x = -7
5) x = 8
6) x = -1
7) x = 4/7
8) x = -4
9) x = -5
10) x = -5