Here is the complete solution to the worksheet
“Solving Linear Equations with the Distributive Property”, broken down by section and problem, with step-by-step explanations.
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✔ SECTION A: Expand brackets and solve
1) 3(x + 6) = 27
Expand:
3x + 18 = 27
Subtract 18:
3x = 9
Divide by 3:
x = 3
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2) 2(x + 4) = 22
Expand:
2x + 8 = 22
Subtract 8:
2x = 14
Divide by 2:
x = 7
---
3) 6(x – 5) = 42
Expand:
6x – 30 = 42
Add 30:
6x = 72
Divide by 6:
x = 12
---
4) 2(x – 3) = 16
Expand:
2x – 6 = 16
Add 6:
2x = 22
Divide by 2:
x = 11
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5) 4(2x + 5) = 36
Expand:
8x + 20 = 36
Subtract 20:
8x = 16
Divide by 8:
x = 2
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6) 8(3x – 2) = 80
Expand:
24x – 16 = 80
Add 16:
24x = 96
Divide by 24:
x = 4
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7) 3(6x – 7) = 15
Expand:
18x – 21 = 15
Add 21:
18x = 36
Divide by 18:
x = 2
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8) 9(7x + 1) = 72
Expand:
63x + 9 = 72
Subtract 9:
63x = 63
Divide by 63:
x = 1
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9) 4(3x + 5) = 8
Expand:
12x + 20 = 8
Subtract 20:
12x = -12
Divide by 12:
x = -1
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10) 2(4x + 2) = -12
Expand:
8x + 4 = -12
Subtract 4:
8x = -16
Divide by 8:
x = -2
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11) 10(3x – 1) = -100
Expand:
30x – 10 = -100
Add 10:
30x = -90
Divide by 30:
x = -3
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12) 12(2x + 7) = 96
Expand:
24x + 84 = 96
Subtract 84:
24x = 12
Divide by 24:
x = 0.5 or
½
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##
✔ SECTION B: Equations with fractions — Multiply both sides to eliminate denominator first
1) (x + 8)/2 = 9
Multiply both sides by 2:
x + 8 = 18
Subtract 8:
x = 10
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2) (x + 6)/5 = 7
Multiply both sides by 5:
x + 6 = 35
Subtract 6:
x = 29
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3) (2x + 5)/3 = 9
Multiply both sides by 3:
2x + 5 = 27
Subtract 5:
2x = 22
Divide by 2:
x = 11
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4) [6(7x + 2)] / 9 = 6
Multiply both sides by 9:
6(7x + 2) = 54
Expand:
42x + 12 = 54
Subtract 12:
42x = 42
Divide by 42:
x = 1
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5) [2(3x + 4)] / 7 = -4
Multiply both sides by 7:
2(3x + 4) = -28
Expand:
6x + 8 = -28
Subtract 8:
6x = -36
Divide by 6:
x = -6
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6) [3(4x – 6)] / 9 = -6
Multiply both sides by 9:
3(4x – 6) = -54
Expand:
12x – 18 = -54
Add 18:
12x = -36
Divide by 12:
x = -3
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7) (1/2)(4x + 6) = 9
This is the same as:
(4x + 6)/2 = 9
Multiply both sides by 2:
4x + 6 = 18
Subtract 6:
4x = 12
Divide by 4:
x = 3
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8) (1/2)(2x + 12) = 1
Same as:
(2x + 12)/2 = 1
Multiply both sides by 2:
2x + 12 = 2
Subtract 12:
2x = -10
Divide by 2:
x = -5
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9) (1/2)(3x + 5) = 13
Same as:
(3x + 5)/2 = 13
Multiply both sides by 2:
3x + 5 = 26
Subtract 5:
3x = 21
Divide by 3:
x = 7
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## 📝 FINAL ANSWERS:
Section A:
1)
3
2)
7
3)
12
4)
11
5)
2
6)
4
7)
2
8)
1
9)
-1
10)
-2
11)
-3
12)
0.5 or
½
Section B:
1)
10
2)
29
3)
11
4)
1
5)
-6
6)
-3
7)
3
8)
-5
9)
7
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✔ All problems solved using the distributive property and inverse operations. Let me know if you’d like a printable version or explanation for any specific problem!
Parent Tip: Review the logic above to help your child master the concept of solving equations with distributive property worksheet.
