Let’s solve each equation step by step. We’ll isolate the variable
x on one side of the equation and simplify carefully. Remember to round to the nearest hundredth if needed.
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1) -8 + 5x = 2 + 7(9 - 3x)
First, distribute the 7 on the right:
→ -8 + 5x = 2 + 63 - 21x
→ -8 + 5x = 65 - 21x
Now add 21x to both sides:
→ -8 + 26x = 65
Add 8 to both sides:
→ 26x = 73
Divide by 26:
→ x = 73 ÷ 26 ≈ 2.807... →
2.81
✔ Matches given answer.
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2) 5 + 2x = 5x - 2x
Simplify right side: 5x - 2x = 3x
→ 5 + 2x = 3x
Subtract 2x from both sides:
→ 5 = x
So,
x = 5.00
✔ Matches given answer.
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3) 3x + 4 = -9(-5x + 5)
Distribute -9 on the right:
→ 3x + 4 = 45x - 45
Subtract 3x from both sides:
→ 4 = 42x - 45
Add 45 to both sides:
→ 49 = 42x
Divide by 42:
→ x = 49 ÷ 42 ≈ 1.166... →
1.17
✔ Matches given answer.
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4) -3(7 + 3x) = -7(8x - 4)
Distribute both sides:
Left: -21 - 9x
Right: -56x + 28
Equation becomes:
→ -21 - 9x = -56x + 28
Add 56x to both sides:
→ -21 + 47x = 28
Add 21 to both sides:
→ 47x = 49
Divide by 47:
→ x = 49 ÷ 47 ≈ 1.042... →
1.04
✔ Matches given answer.
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5) -2x - 2 = -6 - 5x
Add 5x to both sides:
→ 3x - 2 = -6
Add 2 to both sides:
→ 3x = -4
Divide by 3:
→ x = -4 ÷ 3 ≈ -1.333... →
-1.33
✔ Matches given answer.
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6) 3(3x - 6) = 4x + 7
Distribute left side:
→ 9x - 18 = 4x + 7
Subtract 4x from both sides:
→ 5x - 18 = 7
Add 18 to both sides:
→ 5x = 25
Divide by 5:
→ x = 5.00
✔ Matches given answer.
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7) 2x - 2(-5 + 2x) = 5x - 3x
Simplify right side: 5x - 3x = 2x
Left side: distribute -2 → 2x + 10 - 4x = -2x + 10
Equation becomes:
→ -2x + 10 = 2x
Add 2x to both sides:
→ 10 = 4x
Divide by 4:
→ x = 2.50
✔ Matches given answer.
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8) 2x + 5(-5x - 4) = -7(-2x + 8) - 3
Distribute both sides:
Left: 2x -25x -20 = -23x -20
Right: 14x -56 -3 = 14x -59
Equation:
→ -23x -20 = 14x -59
Add 23x to both sides:
→ -20 = 37x -59
Add 59 to both sides:
→ 39 = 37x
Divide by 37:
→ x = 39 ÷ 37 ≈ 1.054... →
1.05
✔ Matches given answer.
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9) -4(x + 5) - 2(x - 6) = 3x + 8
Distribute:
Left: -4x -20 -2x +12 = -6x -8
Right: 3x + 8
Equation:
→ -6x -8 = 3x + 8
Add 6x to both sides:
→ -8 = 9x + 8
Subtract 8:
→ -16 = 9x
Divide by 9:
→ x = -16 ÷ 9 ≈ -1.777... →
-1.78
✔ Matches given answer.
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10) 2 - 5x = 3(x - 6)
Distribute right side:
→ 2 - 5x = 3x - 18
Add 5x to both sides:
→ 2 = 8x - 18
Add 18:
→ 20 = 8x
Divide by 8:
→ x = 20 ÷ 8 = 2.50
✔ Matches given answer.
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All answers are correct as shown in the worksheet.
Final Answer:
All equations have been solved correctly with the following solutions:
1) x = 2.81
2) x = 5.00
3) x = 1.17
4) x = 1.04
5) x = -1.33
6) x = 5.00
7) x = 2.50
8) x = 1.05
9) x = -1.78
10) x = 2.50
Parent Tip: Review the logic above to help your child master the concept of solving linear equations variable on both sides worksheet.
