Math worksheet for practicing solving equations using the distributive property, with ten problems requiring students to find the value of x.

We are given 10 equations to solve using the Distributive Property. The distributive property states:

> a(b + c) = ab + ac

We’ll apply this to each equation, simplify, and then solve for x.

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① 5(4x + 8) = 80

Step 1: Distribute the 5
→ 5·4x + 5·8 = 80
→ 20x + 40 = 80

Step 2: Subtract 40 from both sides
→ 20x = 40

Step 3: Divide by 20
→ x = 2

✔ Answer: x = 2

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② -4x = 3(x + 7)

Step 1: Distribute the 3 on the right
→ -4x = 3x + 21

Step 2: Subtract 3x from both sides
→ -7x = 21

Step 3: Divide by -7
→ x = -3

✔ Answer: x = -3

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③ 2(x - 1) + 3x = 3

Step 1: Distribute the 2
→ 2x - 2 + 3x = 3

Step 2: Combine like terms
→ 5x - 2 = 3

Step 3: Add 2 to both sides
→ 5x = 5

Step 4: Divide by 5
→ x = 1

✔ Answer: x = 1

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④ (3/2)(3x + 5) = -24

Step 1: Distribute 3/2
→ (3/2)·3x + (3/2)·5 = -24
→ (9/2)x + 15/2 = -24

Step 2: Multiply entire equation by 2 to eliminate denominators
→ 9x + 15 = -48

Step 3: Subtract 15
→ 9x = -63

Step 4: Divide by 9
→ x = -7

✔ Answer: x = -7

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⑤ 3(x - 2) = 18

Step 1: Distribute the 3
→ 3x - 6 = 18

Step 2: Add 6
→ 3x = 24

Step 3: Divide by 3
→ x = 8

✔ Answer: x = 8

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⑥ 0.25(3 + x) = 0.5

Step 1: Distribute 0.25
→ 0.25·3 + 0.25·x = 0.5
→ 0.75 + 0.25x = 0.5

Step 2: Subtract 0.75
→ 0.25x = -0.25

Step 3: Divide by 0.25
→ x = -1

✔ Answer: x = -1

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⑦ 2(3x - 1) + 2(4x + 5) = 16

Step 1: Distribute both 2s
→ 6x - 2 + 8x + 10 = 16

Step 2: Combine like terms
→ 14x + 8 = 16

Step 3: Subtract 8
→ 14x = 8

Step 4: Divide by 14
→ x = 8/14 = 4/7

✔ Answer: x = 4/7

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⑧ -2 - 3(1 - 4x) = -53

Step 1: Distribute the -3
→ -2 -3·1 + (-3)·(-4x) = -53
→ -2 -3 + 12x = -53
→ 12x - 5 = -53

Step 2: Add 5
→ 12x = -48

Step 3: Divide by 12
→ x = -4

✔ Answer: x = -4

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⑨ -111 = 3(7x - 2)

Step 1: Distribute the 3
→ -111 = 21x - 6

Step 2: Add 6 to both sides
→ -105 = 21x

Step 3: Divide by 21
→ x = -5

✔ Answer: x = -5

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⑩ -86 = 4 + 5(3x - 3)

Step 1: Distribute the 5
→ -86 = 4 + 15x - 15
→ -86 = 15x - 11

Step 2: Add 11 to both sides
→ -75 = 15x

Step 3: Divide by 15
→ x = -5

✔ Answer: x = -5

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## ✔ Final Answers:

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

Let me know if you’d like step-by-step work shown in a different format!