Let’s solve each equation step by step. We’ll isolate the variable (usually x) on one side and constants on the other.
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1.) x + 142 = 16x + 7
Subtract x from both sides:
142 = 15x + 7
Subtract 7 from both sides:
135 = 15x
Divide by 15:
x = 9
✔ Check: Left: 9 + 142 = 151; Right: 16*9 + 7 = 144 + 7 = 151 → Correct!
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2.) 8x = 2x - 6
Subtract 2x from both sides:
6x = -6
Divide by 6:
x = -1
✔ Check: Left: 8*(-1) = -8; Right: 2*(-1) - 6 = -2 - 6 = -8 → Correct!
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3.) 1 + 9x = 7 + 8x
Subtract 8x from both sides:
1 + x = 7
Subtract 1:
x = 6
✔ Check: Left: 1 + 54 = 55; Right: 7 + 48 = 55 → Correct!
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4.) -8x + 8 = 10 + 5 - 9x
Simplify right side: 10 + 5 = 15 → -8x + 8 = 15 - 9x
Add 9x to both sides:
x + 8 = 15
Subtract 8:
x = 7
✔ Check: Left: -56 + 8 = -48; Right: 15 - 63 = -48 → Correct!
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5.) 7x + 2 = -10x + 2
Add 10x to both sides:
17x + 2 = 2
Subtract 2:
17x = 0
Divide by 17:
x = 0
✔ Check: Both sides = 2 → Correct!
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6.) 55 - x = 2x + 13
Add x to both sides:
55 = 3x + 13
Subtract 13:
42 = 3x
Divide by 3:
x = 14
✔ Check: Left: 55 - 14 = 41; Right: 28 + 13 = 41 → Correct!
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7.) -3x - 4x = -8x + 1
Combine left: -7x = -8x + 1
Add 8x:
x = 1
✔ Check: Left: -3 -4 = -7; Right: -8 + 1 = -7 → Correct!
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8.) 5 - 5x + 6 = 4 - 4x
Left: 11 - 5x = 4 - 4x
Add 5x:
11 = 4 + x
Subtract 4:
x = 7
✔ Check: Left: 5 -35 +6 = -24; Right: 4 -28 = -24 → Correct!
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9.) 7x - 5 = 9x + 9
Subtract 7x:
-5 = 2x + 9
Subtract 9:
-14 = 2x
Divide by 2:
x = -7
✔ Check: Left: -49 -5 = -54; Right: -63 + 9 = -54 → Correct!
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10.) -20 - 8x = 5x - 7
Add 8x:
-20 = 13x - 7
Add 7:
-13 = 13x
Divide by 13:
x = -1
✔ Check: Left: -20 +8 = -12; Right: -5 -7 = -12 → Correct!
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11.) 100 - x = 6 + 11x + 10
Right: 16 + 11x
So: 100 - x = 16 + 11x
Add x:
100 = 16 + 12x
Subtract 16:
84 = 12x
Divide by 12:
x = 7
✔ Check: Left: 100 -7 = 93; Right: 6 + 77 + 10 = 93 → Correct!
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12.) -5 + 5x = 10x + 4 - 6x
Right: 4x + 4
So: -5 + 5x = 4x + 4
Subtract 4x:
-5 + x = 4
Add 5:
x = 9
✔ Check: Left: -5 + 45 = 40; Right: 90 + 4 - 54 = 40 → Correct!
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13.) x - 9 - 5x = 2 - 5x
Left: -4x - 9 = 2 - 5x
Add 5x:
x - 9 = 2
Add 9:
x = 11
✔ Check: Left: 11 -9 -55 = -53; Right: 2 -55 = -53 → Correct!
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14.) 38 + 12x = 44 - x
Add x:
38 + 13x = 44
Subtract 38:
13x = 6
Divide by 13:
x = 6/13
✔ Check: Left: 38 + 72/13 = (494 + 72)/13 = 566/13; Right: 44 - 6/13 = (572 - 6)/13 = 566/13 → Correct!
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15.) 3x - 10 = 4x - 8
Subtract 3x:
-10 = x - 8
Add 8:
-2 = x
x = -2
✔ Check: Left: -6 -10 = -16; Right: -8 -8 = -16 → Correct!
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16.) x + 2 = 2x + 14
Subtract x:
2 = x + 14
Subtract 14:
-12 = x
x = -12
✔ Check: Left: -12 + 2 = -10; Right: -24 + 14 = -10 → Correct!
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Final Answer:
1.) 9
2.) -1
3.) 6
4.) 7
5.) 0
6.) 14
7.) 1
8.) 7
9.) -7
10.) -1
11.) 7
12.) 9
13.) 11
14.) 6/13
15.) -2
16.) -12
Parent Tip: Review the logic above to help your child master the concept of grade 8 math worksheet printable.
