Let’s solve each equation one by one. We’ll find the value of the variable in each problem, and then we can match it to the numbers in the picture (though since you didn’t ask for shading, we’ll just focus on solving).
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1. x + 3(x + 4) = 20
First, distribute the 3:
x + 3x + 12 = 20
Combine like terms:
4x + 12 = 20
Subtract 12 from both sides:
4x = 8
Divide by 4:
x = 2
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2. 6(y - 1) + 8 = 32
Distribute the 6:
6y - 6 + 8 = 32
Simplify:
6y + 2 = 32
Subtract 2:
6y = 30
Divide by 6:
y = 5
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3. 5 + 4(n + 9) = -3
Distribute the 4:
5 + 4n + 36 = -3
Combine:
4n + 41 = -3
Subtract 41:
4n = -44
Divide by 4:
n = -11
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4. 5(k - 2) - 8k = -34
Distribute the 5:
5k - 10 - 8k = -34
Combine like terms:
-3k - 10 = -34
Add 10:
-3k = -24
Divide by -3:
k = 8
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5. 2 = 11 + 3(m + 3)
Distribute the 3:
2 = 11 + 3m + 9
Combine:
2 = 3m + 20
Subtract 20:
-18 = 3m
Divide by 3:
m = -6
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6. -2(p - 5) + 7p = -5
Distribute the -2:
-2p + 10 + 7p = -5
Combine:
5p + 10 = -5
Subtract 10:
5p = -15
Divide by 5:
p = -3
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7. 4a - 2(a + 9) = 6
Distribute the -2:
4a - 2a - 18 = 6
Combine:
2a - 18 = 6
Add 18:
2a = 24
Divide by 2:
a = 12
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8. 7 - 4(d - 3) = 23
Distribute the -4:
7 - 4d + 12 = 23
Combine:
19 - 4d = 23
Subtract 19:
-4d = 4
Divide by -4:
d = -1
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9. 8x - 11(x - 2) = -8
Distribute the -11:
8x - 11x + 22 = -8
Combine:
-3x + 22 = -8
Subtract 22:
-3x = -30
Divide by -3:
x = 10
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10. 5 = 6(q - 5) - 19
Distribute the 6:
5 = 6q - 30 - 19
Combine:
5 = 6q - 49
Add 49:
54 = 6q
Divide by 6:
q = 9
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11. 3(3 - y) + 1 = 31
Distribute the 3:
9 - 3y + 1 = 31
Combine:
10 - 3y = 31
Subtract 10:
-3y = 21
Divide by -3:
y = -7
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12. 5(2v + 4) = 170
Distribute the 5:
10v + 20 = 170
Subtract 20:
10v = 150
Divide by 10:
v = 15
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13. 5(4n - 4) = -60
Distribute the 5:
20n - 20 = -60
Add 20:
20n = -40
Divide by 20:
n = -2
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14. 2(3t - 8) - 4t = 10
Distribute the 2:
6t - 16 - 4t = 10
Combine:
2t - 16 = 10
Add 16:
2t = 26
Divide by 2:
t = 13
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15. 9 - 4(2p - 1) = 45
Distribute the -4:
9 - 8p + 4 = 45
Combine:
13 - 8p = 45
Subtract 13:
-8p = 32
Divide by -8:
p = -4
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16. Area of rectangle is 70 square units. Sides are 7 and (x + 4).
Area = length × width
7 × (x + 4) = 70
Divide both sides by 7:
x + 4 = 10
Subtract 4:
x = 6
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17. Area of rectangle is 55 square units. Sides are 5 and (3x - 1).
Area = length × width
5 × (3x - 1) = 55
Divide both sides by 5:
3x - 1 = 11
Add 1:
3x = 12
Divide by 3:
x = 4
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Final Answer:
Here are all the solutions:
1. x = 2
2. y = 5
3. n = -11
4. k = 8
5. m = -6
6. p = -3
7. a = 12
8. d = -1
9. x = 10
10. q = 9
11. y = -7
12. v = 15
13. n = -2
14. t = 13
15. p = -4
16. x = 6
17. x = 4
Parent Tip: Review the logic above to help your child master the concept of bridge to algebra worksheet answers.
