Let’s solve each equation step by step using the distributive property and then isolating the variable.
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1) 2(a + 3) = -12
Distribute:
2·a + 2·3 = -12 → 2a + 6 = -12
Subtract 6 from both sides:
2a = -18
Divide by 2:
a = -9
✔ Check: 2(-9 + 3) = 2(-6) = -12 ✔️
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2) 3(p + 2) = 18
Distribute:
3p + 6 = 18
Subtract 6:
3p = 12
Divide by 3:
p = 4
✔ Check: 3(4 + 2) = 3(6) = 18 ✔️
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3) 4(2r + 8) = 88
Distribute:
8r + 32 = 88
Subtract 32:
8r = 56
Divide by 8:
r = 7
✔ Check: 4(2·7 + 8) = 4(14 + 8) = 4(22) = 88 ✔️
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4) 2(3a + 2) = -8
Distribute:
6a + 4 = -8
Subtract 4:
6a = -12
Divide by 6:
a = -2
✔ Check: 2(3·-2 + 2) = 2(-6 + 2) = 2(-4) = -8 ✔️
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5) 4 = 4(k + 3)
Distribute right side:
4 = 4k + 12
Subtract 12 from both sides:
-8 = 4k
Divide by 4:
k = -2
✔ Check: 4 = 4(-2 + 3) = 4(1) = 4 ✔️
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6) 5 = 5(y - 2)
Distribute:
5 = 5y - 10
Add 10 to both sides:
15 = 5y
Divide by 5:
y = 3
✔ Check: 5 = 5(3 - 2) = 5(1) = 5 ✔️
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7) -(3k - 12) = 48
This is the same as multiplying by -1:
-3k + 12 = 48
Subtract 12:
-3k = 36
Divide by -3:
k = -12
✔ Check: -(3·-12 - 12) = -(-36 - 12) = -(-48) = 48 ✔️
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8) -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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9) (1/2)(4x - 6) = 11
Multiply both sides by 2 to eliminate fraction:
4x - 6 = 22
Add 6:
4x = 28
Divide by 4:
x = 7
✔ Check: (1/2)(4·7 - 6) = (1/2)(28 - 6) = (1/2)(22) = 11 ✔️
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10) (2/3)(6x - 9) = -34
Multiply both sides by 3 to eliminate denominator:
2(6x - 9) = -102
Distribute:
12x - 18 = -102
Add 18:
12x = -84
Divide by 12:
x = -7
✔ Check: (2/3)(6·-7 - 9) = (2/3)(-42 - 9) = (2/3)(-51) = -34 ✔️
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Final Answer:
1) a = -9
2) p = 4
3) r = 7
4) a = -2
5) k = -2
6) y = 3
7) k = -12
8) x = -12
9) x = 7
10) x = -7
Parent Tip: Review the logic above to help your child master the concept of solving equations with distributive property worksheet.
