Let’s solve each equation step by step.
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1. x + 9 = 8
Subtract 9 from both sides:
x = 8 - 9
x = -1
✔ Check: -1 + 9 = 8 → Correct.
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2. 8 + 2x = 10
Subtract 8 from both sides:
2x = 2
Divide by 2:
x = 1
✔ Check: 8 + 2(1) = 10 → Correct.
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3. 5(4x + 2) = -30
First, divide both sides by 5:
4x + 2 = -6
Subtract 2:
4x = -8
Divide by 4:
x = -2
✔ Check: 5(4*(-2)+2) = 5(-8+2) = 5(-6) = -30 → Correct.
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4. 13x + 5x = 9
Combine like terms:
18x = 9
Divide by 18:
x = 9/18 = 1/2
✔ Check: 13*(1/2) + 5*(1/2) = 18/2 = 9 → Correct.
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5. 3(y + 4) + 2 = 11
Distribute:
3y + 12 + 2 = 11
Simplify:
3y + 14 = 11
Subtract 14:
3y = -3
Divide by 3:
y = -1
✔ Check: 3(-1+4)+2 = 3(3)+2 = 9+2=11 → Correct.
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6. 5x - 6 = -12x + 8
Add 12x to both sides:
17x - 6 = 8
Add 6:
17x = 14
Divide by 17:
x = 14/17
✔ Check: Left: 5*(14/17) - 6 = 70/17 - 102/17 = -32/17
Right: -12*(14/17) + 8 = -168/17 + 136/17 = -32/17 → Correct.
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7. 7x + 4 = 10 - 8(x + 4)
Distribute on right:
7x + 4 = 10 - 8x - 32
Simplify right:
7x + 4 = -8x - 22
Add 8x:
15x + 4 = -22
Subtract 4:
15x = -26
x = -26/15
✔ Check:
Left: 7*(-26/15) + 4 = -182/15 + 60/15 = -122/15
Right: 10 - 8*(-26/15 + 60/15) = 10 - 8*(34/15) = 10 - 272/15 = 150/15 - 272/15 = -122/15 → Correct.
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8. (11x - 4)/2 = 15
Multiply both sides by 2:
11x - 4 = 30
Add 4:
11x = 34
x = 34/11
✔ Check: (11*(34/11) - 4)/2 = (34 - 4)/2 = 30/2 = 15 → Correct.
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9. 9x + 2(3x - 5) = 3(3x + 4)
Distribute:
9x + 6x - 10 = 9x + 12
Combine left:
15x - 10 = 9x + 12
Subtract 9x:
6x - 10 = 12
Add 10:
6x = 22
x = 22/6 = 11/3
✔ Check:
Left: 9*(11/3) + 2(3*(11/3)-5) = 33 + 2(11-5) = 33 + 12 = 45
Right: 3(3*(11/3)+4) = 3(11+4) = 3*15 = 45 → Correct.
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10. 4(3y - 5) = 4(2y + 4)
Divide both sides by 4 (since 4 ≠ 0):
3y - 5 = 2y + 4
Subtract 2y:
y - 5 = 4
Add 5:
y = 9
✔ Check:
Left: 4(27 - 5) = 4*22 = 88
Right: 4(18 + 4) = 4*22 = 88 → Correct.
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Final Answer:
1. x = -1
2. x = 1
3. x = -2
4. x = 1/2
5. y = -1
6. x = 14/17
7. x = -26/15
8. x = 34/11
9. x = 11/3
10. y = 9
Parent Tip: Review the logic above to help your child master the concept of solving algebraic equations worksheets.
