Let’s solve each equation step by step. We’ll go one at a time, carefully simplifying and isolating the variable.
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1. 7c – 3 + 2c = 15
Combine like terms on the left:
7c + 2c = 9c → so we have:
9c – 3 = 15
Add 3 to both sides:
9c = 18
Divide by 9:
c = 2
✔ Check: 7(2) – 3 + 2(2) = 14 – 3 + 4 = 15 ✔️
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2. 5(x – 7) = 20
Distribute the 5:
5x – 35 = 20
Add 35 to both sides:
5x = 55
Divide by 5:
x = 11
✔ Check: 5(11 – 7) = 5(4) = 20 ✔️
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3. 6h + 5 = 10 + h
Subtract h from both sides:
5h + 5 = 10
Subtract 5 from both sides:
5h = 5
Divide by 5:
h = 1
✔ Check: 6(1) + 5 = 11; 10 + 1 = 11 ✔️
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4. 60 = -4(3y – 6)
Distribute the -4:
60 = -12y + 24
Subtract 24 from both sides:
36 = -12y
Divide by -12:
y = -3
✔ Check: -4(3*(-3) – 6) = -4(-9 – 6) = -4(-15) = 60 ✔️
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5. -5g + 24 = 7g – 24
Add 5g to both sides:
24 = 12g – 24
Add 24 to both sides:
48 = 12g
Divide by 12:
g = 4
✔ Check: -5(4)+24= -20+24=4; 7(4)-24=28-24=4 ✔️
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6. 22 = 3u + 10 – 5u
Combine like terms on right:
3u – 5u = -2u → so:
22 = -2u + 10
Subtract 10 from both sides:
12 = -2u
Divide by -2:
u = -6
✔ Check: 3(-6)+10–5(-6)= -18+10+30=22 ✔️
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7. -5(3k – 3) + 17 = -43
Distribute -5:
-15k + 15 + 17 = -43
Combine constants:
-15k + 32 = -43
Subtract 32 from both sides:
-15k = -75
Divide by -15:
k = 5
✔ Check: -5(15–3)+17 = -5(12)+17 = -60+17=-43 ✔️
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8. 7t – 5 + 4t = 3t – 21
Combine like terms on left:
11t – 5 = 3t – 21
Subtract 3t from both sides:
8t – 5 = -21
Add 5 to both sides:
8t = -16
Divide by 8:
t = -2
✔ Check: 7(-2)–5+4(-2)= -14–5–8=-27; 3(-2)–21=-6–21=-27 ✔️
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9. 5m – 7 = 3(2m + 1)
Distribute 3 on right:
5m – 7 = 6m + 3
Subtract 5m from both sides:
-7 = m + 3
Subtract 3 from both sides:
-10 = m
So m = -10
✔ Check: 5(-10)–7=-50–7=-57; 3(2*(-10)+1)=3(-20+1)=3(-19)=-57 ✔️
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10. -12 = 4(2q + 7) – 3q
Distribute 4:
-12 = 8q + 28 – 3q
Combine like terms:
-12 = 5q + 28
Subtract 28 from both sides:
-40 = 5q
Divide by 5:
q = -8
✔ Check: 4(2*(-8)+7) – 3*(-8) = 4(-16+7) +24 = 4(-9)+24 = -36+24=-12 ✔️
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11. -11 – 6b + 3 = 16 + 2b
Combine constants on left:
-8 – 6b = 16 + 2b
Add 6b to both sides:
-8 = 16 + 8b
Subtract 16 from both sides:
-24 = 8b
Divide by 8:
b = -3
✔ Check: -11–6(-3)+3 = -11+18+3=10; 16+2(-3)=16–6=10 ✔️
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12. 5(8 – 2w) = 4 – 4w
Distribute 5:
40 – 10w = 4 – 4w
Add 10w to both sides:
40 = 4 + 6w
Subtract 4 from both sides:
36 = 6w
Divide by 6:
w = 6
✔ Check: 5(8–12)=5(-4)=-20; 4–4(6)=4–24=-20 ✔️
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Final Answer:
1. c = 2
2. x = 11
3. h = 1
4. y = -3
5. g = 4
6. u = -6
7. k = 5
8. t = -2
9. m = -10
10. q = -8
11. b = -3
12. w = 6
Parent Tip: Review the logic above to help your child master the concept of multi step equations worksheets.
