Worksheet for practicing solving equations with the distributive property.

Let’s solve each equation step by step using the distributive property and inverse operations. We’ll go one at a time.

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Problem 1: -10(x + 2) = 73

Step 1: Distribute -10 to both terms inside the parentheses
→ -10 * x = -10x
→ -10 * 2 = -20
So: -10x - 20 = 73

Step 2: Add 20 to both sides to get rid of -20 on the left
→ -10x - 20 + 20 = 73 + 20
→ -10x = 93

Step 3: Divide both sides by -10
→ x = 93 / (-10)
→ x = -9.3

✔ Check: Plug back in → -10(-9.3 + 2) = -10(-7.3) = 73 ✔️

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Problem 2: 1 + 3(4f – 5) = 28

Step 1: Distribute 3 to both terms inside parentheses
→ 3 * 4f = 12f
→ 3 * (-5) = -15
So: 1 + 12f - 15 = 28

Step 2: Combine like terms on left (1 - 15)
→ 12f - 14 = 28

Step 3: Add 14 to both sides
→ 12f = 28 + 14
→ 12f = 42

Step 4: Divide both sides by 12
→ f = 42 / 12
→ Simplify: divide numerator and denominator by 6 → f = 3.5 or 7/2

✔ Check: 1 + 3(4*3.5 - 5) = 1 + 3(14 - 5) = 1 + 3(9) = 1 + 27 = 28 ✔️

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Problem 3: 8(3r – 1) = r – 57

Step 1: Distribute 8
→ 8 * 3r = 24r
→ 8 * (-1) = -8
So: 24r - 8 = r - 57

Step 2: Subtract r from both sides to get all variables on left
→ 24r - r - 8 = -57
→ 23r - 8 = -57

Step 3: Add 8 to both sides
→ 23r = -57 + 8
→ 23r = -49

Step 4: Divide by 23
→ r = -49/23

This doesn’t simplify further, so leave as fraction.

✔ Check: Left side: 8(3*(-49/23) - 1) = 8(-147/23 - 23/23) = 8(-170/23) = -1360/23
Right side: -49/23 - 57 = -49/23 - 1311/23 = -1360/23 ✔️

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Problem 4: -4(2a – 1) = 5 + 83

Wait — right side is just numbers: 5 + 83 = 88
So equation is: -4(2a – 1) = 88

Step 1: Distribute -4
→ -4 * 2a = -8a
→ -4 * (-1) = +4
So: -8a + 4 = 88

Step 2: Subtract 4 from both sides
→ -8a = 84

Step 3: Divide by -8
→ a = 84 / (-8) = -10.5 or -21/2

✔ Check: -4(2*(-10.5) - 1) = -4(-21 - 1) = -4(-22) = 88 ✔️

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Problem 5: -4 + 7(3s + 3) = 52

Step 1: Distribute 7
→ 7 * 3s = 21s
→ 7 * 3 = 21
So: -4 + 21s + 21 = 52

Step 2: Combine constants: -4 + 21 = 17
→ 21s + 17 = 52

Step 3: Subtract 17 from both sides
→ 21s = 35

Step 4: Divide by 21
→ s = 35/21 = 5/3 (divide top and bottom by 7)

✔ Check: -4 + 7(3*(5/3) + 3) = -4 + 7(5 + 3) = -4 + 7*8 = -4 + 56 = 52 ✔️

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Problem 6: -2 – 3(2m – 5) = 60

Step 1: Distribute -3
→ -3 * 2m = -6m
→ -3 * (-5) = +15
So: -2 -6m + 15 = 60

Step 2: Combine constants: -2 + 15 = 13
→ -6m + 13 = 60

Step 3: Subtract 13 from both sides
→ -6m = 47

Step 4: Divide by -6
→ m = 47 / (-6) = -47/6

✔ Check: -2 -3(2*(-47/6) - 5) = -2 -3(-94/6 - 30/6) = -2 -3(-124/6) = -2 + 372/6 = -2 + 62 = 60 ✔️

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Problem 7: 2(7t + 8) = 6t – 48

Step 1: Distribute 2
→ 2 * 7t = 14t
→ 2 * 8 = 16
So: 14t + 16 = 6t – 48

Step 2: Subtract 6t from both sides
→ 8t + 16 = -48

Step 3: Subtract 16 from both sides
→ 8t = -64

Step 4: Divide by 8
→ t = -8

✔ Check: 2(7*(-8)+8) = 2(-56+8)=2(-48)=-96; Right: 6*(-8)-48=-48-48=-96 ✔️

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Problem 8: -5(-2d + 5) = 13 + 4d

Step 1: Distribute -5
→ -5 * -2d = +10d
→ -5 * 5 = -25
So: 10d - 25 = 13 + 4d

Step 2: Subtract 4d from both sides
→ 6d - 25 = 13

Step 3: Add 25 to both sides
→ 6d = 38

Step 4: Divide by 6
→ d = 38/6 = 19/3

✔ Check: Left: -5(-2*(19/3)+5) = -5(-38/3 + 15/3) = -5(-23/3) = 115/3
Right: 13 + 4*(19/3) = 39/3 + 76/3 = 115/3 ✔️

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Problem 9: 4(-8g + 1) = -20g + 8

Step 1: Distribute 4
→ 4 * -8g = -32g
→ 4 * 1 = 4
So: -32g + 4 = -20g + 8

Step 2: Add 32g to both sides
→ 4 = 12g + 8

Step 3: Subtract 8 from both sides
→ -4 = 12g

Step 4: Divide by 12
→ g = -4/12 = -1/3

✔ Check: Left: 4(-8*(-1/3)+1) = 4(8/3 + 3/3) = 4(11/3) = 44/3
Right: -20*(-1/3) + 8 = 20/3 + 24/3 = 44/3 ✔️

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Final Answer:

1. x = -9.3
2. f = 3.5 (or 7/2)
3. r = -49/23
4. a = -10.5 (or -21/2)
5. s = 5/3
6. m = -47/6
7. t = -8
8. d = 19/3
9. g = -1/3