Let’s solve each equation step by step. We’ll isolate the variable and round to the nearest hundredth as instructed.
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1) (6.6 + y) / (-6.2) = 2.5
Multiply both sides by -6.2:
6.6 + y = 2.5 × (-6.2)
6.6 + y = -15.5
Subtract 6.6 from both sides:
y = -15.5 - 6.6
y = -22.1 →
-22.10
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2) (c - 4.4) / 7.7 = 9.2
Multiply both sides by 7.7:
c - 4.4 = 9.2 × 7.7
c - 4.4 = 70.84
Add 4.4 to both sides:
c = 70.84 + 4.4
c = 75.24 →
75.24
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3) (d + 4.1) / (-5.3) = -4.3
Multiply both sides by -5.3:
d + 4.1 = (-4.3) × (-5.3)
d + 4.1 = 22.79
Subtract 4.1:
d = 22.79 - 4.1
d = 18.69 →
18.69
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4) (4.8 - f) / (-3.8) = 9.7
Multiply both sides by -3.8:
4.8 - f = 9.7 × (-3.8)
4.8 - f = -36.86
Subtract 4.8:
-f = -36.86 - 4.8
-f = -41.66
Multiply both sides by -1:
f = 41.66 →
41.66
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5) -6.8 - 4.8b = 5.6
Add 6.8 to both sides:
-4.8b = 5.6 + 6.8
-4.8b = 12.4
Divide by -4.8:
b = 12.4 / (-4.8)
b ≈ -2.5833... →
-2.58
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6) -7.7n - 6.7 = 9.2
Add 6.7 to both sides:
-7.7n = 9.2 + 6.7
-7.7n = 15.9
Divide by -7.7:
n = 15.9 / (-7.7)
n ≈ -2.0649... →
-2.06
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7) -4.2 + (6/7)a = 8.9
Add 4.2 to both sides:
(6/7)a = 8.9 + 4.2
(6/7)a = 13.1
Multiply both sides by 7/6:
a = 13.1 × (7/6)
a = 91.7 / 6
a ≈ 15.2833... →
15.28
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8) (k - 9.8) / (-9.3) = 7.7
Multiply both sides by -9.3:
k - 9.8 = 7.7 × (-9.3)
k - 9.8 = -71.61
Add 9.8:
k = -71.61 + 9.8
k = -61.81 →
-61.81
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9) (4.9 + r) / 4.6 = 7.1
Multiply both sides by 4.6:
4.9 + r = 7.1 × 4.6
4.9 + r = 32.66
Subtract 4.9:
r = 32.66 - 4.9
r = 27.76 →
27.76
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10) (1/8)z - 4.8 = 6.2
Add 4.8 to both sides:
(1/8)z = 6.2 + 4.8
(1/8)z = 11
Multiply both sides by 8:
z = 11 × 8
z = 88 →
88.00
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Final Answer:
1) -22.10
2) 75.24
3) 18.69
4) 41.66
5) -2.58
6) -2.06
7) 15.28
8) -61.81
9) 27.76
10) 88.00
Parent Tip: Review the logic above to help your child master the concept of worksheets for 8th graders.
