Let’s solve each equation step by step using the distributive property. The distributive property means we multiply the number outside the parentheses by each term inside the parentheses.
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1) 2(2 + m) = 16
Distribute:
2 × 2 + 2 × m = 16 → 4 + 2m = 16
Subtract 4 from both sides:
2m = 12
Divide by 2:
m = 6
✔ Check: 2(2 + 6) = 2×8 = 16 ✔️
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2) 3(3 + f) = -15
Distribute:
9 + 3f = -15
Subtract 9:
3f = -24
Divide by 3:
f = -8
✔ Check: 3(3 + (-8)) = 3×(-5) = -15 ✔️
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3) 4 = 4(g + 3)
Distribute right side:
4 = 4g + 12
Subtract 12 from both sides:
-8 = 4g
Divide by 4:
g = -2
✔ Check: 4(-2 + 3) = 4×1 = 4 ✔️
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4) -2(x - 3) = 30
Distribute:
-2x + 6 = 30
Subtract 6:
-2x = 24
Divide by -2:
x = -12
✔ Check: -2(-12 - 3) = -2×(-15) = 30 ✔️
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5) 3(c + 5) = 12
Distribute:
3c + 15 = 12
Subtract 15:
3c = -3
Divide by 3:
c = -1
✔ Check: 3(-1 + 5) = 3×4 = 12 ✔️
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6) 6(3x + 5) = 39
Distribute:
18x + 30 = 39
Subtract 30:
18x = 9
Divide by 18:
x = 9/18 = 1/2
✔ Check: 6(3×0.5 + 5) = 6(1.5 + 5) = 6×6.5 = 39 ✔️
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7) 8p - 1 = 6p - 5
This one doesn’t need distribution — it’s already simplified.
Subtract 6p from both sides:
2p - 1 = -5
Add 1 to both sides:
2p = -4
Divide by 2:
p = -2
✔ Check: Left: 8(-2)-1 = -16-1 = -17; Right: 6(-2)-5 = -12-5 = -17 ✔️
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8) 3(2x + 7) = 27
Distribute:
6x + 21 = 27
Subtract 21:
6x = 6
Divide by 6:
x = 1
✔ Check: 3(2×1 + 7) = 3×9 = 27 ✔️
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9) 10(5k + 8) = 10
Distribute:
50k + 80 = 10
Subtract 80:
50k = -70
Divide by 50:
k = -70/50 = -7/5 or -1.4
✔ Check: 10(5×(-1.4) + 8) = 10(-7 + 8) = 10×1 = 10 ✔️
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10) 5(a + 7) = 75
Distribute:
5a + 35 = 75
Subtract 35:
5a = 40
Divide by 5:
a = 8
✔ Check: 5(8 + 7) = 5×15 = 75 ✔️
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Final Answer:
1) m = 6
2) f = -8
3) g = -2
4) x = -12
5) c = -1
6) x = 1/2
7) p = -2
8) x = 1
9) k = -7/5 (or -1.4)
10) a = 8
Parent Tip: Review the logic above to help your child master the concept of distributive property equations worksheet.
