Math worksheet for solving equations using the distributive property, designed for educational practice.

Absolutely! Let’s solve each of the 10 equations step by step using the Distributive Property, which states:

> a(b + c) = ab + ac

We’ll apply this to remove parentheses, then simplify and solve for x.

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① 5(4x + 8) = 80

Step 1: Distribute the 5
→ 5 × 4x = 20x
→ 5 × 8 = 40
So:
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
→ 3 × x = 3x
→ 3 × 7 = 21
So:
-4x = 3x + 21

Step 2: Subtract 3x from both sides
→ -4x - 3x = 21
→ -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
→ 2 × x = 2x
→ 2 × (-1) = -2
So:
2x - 2 + 3x = 3

Step 2: Combine like terms
→ (2x + 3x) - 2 = 3
→ 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 = (9/2)x
→ (3/2) × 5 = 15/2
So:
(9/2)x + 15/2 = -24

Step 2: Subtract 15/2 from both sides
→ (9/2)x = -24 - 15/2
Convert -24 to halves: -24 = -48/2
→ (9/2)x = (-48/2 - 15/2) = -63/2

Step 3: Multiply both sides by 2/9 to isolate x
→ x = (-63/2) × (2/9) = -63/9 = -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 to both sides
→ 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 = 0.75
→ 0.25 × x = 0.25x
So:
0.25x + 0.75 = 0.5

Step 2: Subtract 0.75 from both sides
→ 0.25x = 0.5 - 0.75 = -0.25

Step 3: Divide by 0.25
→ x = -0.25 / 0.25 = -1

✔ Answer: x = -1

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⑦ 2(3x - 1) + 2(4x + 5) = 16

Step 1: Distribute both 2s
→ 2×3x = 6x, 2×(-1) = -2 → first part: 6x - 2
→ 2×4x = 8x, 2×5 = 10 → second part: 8x + 10
So:
6x - 2 + 8x + 10 = 16

Step 2: Combine like terms
→ (6x + 8x) + (-2 + 10) = 16
→ 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
→ -3 × 1 = -3
→ -3 × (-4x) = +12x
So:
-2 - 3 + 12x = -53

Step 2: Combine constants
→ -5 + 12x = -53

Step 3: Add 5 to both sides
→ 12x = -48

Step 4: Divide by 12
→ x = -4

✔ Answer: x = -4

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⑨ -111 = 3(7x - 2)

Step 1: Distribute the 3
→ 3 × 7x = 21x
→ 3 × (-2) = -6
So:
-111 = 21x - 6

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

Step 3: Divide by 21
→ x = -105 / 21 = -5

✔ Answer: x = -5

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⑩ -86 = 4 + 5(3x - 3)

Step 1: Distribute the 5
→ 5 × 3x = 15x
→ 5 × (-3) = -15
So:
-86 = 4 + 15x - 15

Step 2: Simplify right side
→ 4 - 15 = -11
→ -86 = 15x - 11

Step 3: Add 11 to both sides
→ -75 = 15x

Step 4: Divide by 15
→ x = -5

✔ Answer: x = -5

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## ✔ Final Answers Summary:

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 to see any step explained in more detail!