Worksheet for solving two-sided algebraic equations with 16 practice problems.

Let’s solve each of the 16 two-sided algebraic equations step by step. We’ll isolate the variable (usually x) on one side and constants on the other, using inverse operations.

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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: 9 + 142 = 151; 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: 8×(-1) = -8; 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 from both sides:
x = 6

✔ Check: 1 + 54 = 55; 7 + 48 = 55 → Correct.

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4.) -8x + 8 = 10 + 5 - 9x

Simplify right side: 10 + 5 = 15 → so:
-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

x = 0

✔ Check: 0 + 2 = 2; 0 + 2 = 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: 55 - 14 = 41; 2×14 + 13 = 28 + 13 = 41 → Correct.

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7.) -3x - 4x = -8x + 1

Combine left: -7x = -8x + 1

Add 8x to both sides:
x = 1

✔ Check: -3 -4 = -7; -8 + 1 = -7 → Correct.

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8.) 5 - 5x + 6 = 4 - 4x

Combine left: 11 - 5x = 4 - 4x

Add 5x to both sides:
11 = 4 + x

Subtract 4:
x = 7

✔ Check: 5 -35 +6 = -24; 4 -28 = -24 → Correct.

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9.) 7x - 5 = 9x + 9

Subtract 7x:
-5 = 2x + 9

Subtract 9:
-14 = 2x

x = -7

✔ Check: 7×(-7)-5 = -49-5=-54; 9×(-7)+9=-63+9=-54 → Correct.

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10.) -20 - 8x = 5x - 7

Add 8x to both sides:
-20 = 13x - 7

Add 7:
-13 = 13x

x = -1

✔ Check: -20 - (-8) = -12; 5×(-1) -7 = -5-7=-12 → Correct.

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11.) 100 - x = 6 + 11x + 10

Simplify right: 16 + 11x

So: 100 - x = 16 + 11x

Add x:
100 = 16 + 12x

Subtract 16:
84 = 12x

x = 7

✔ Check: 100 - 7 = 93; 6 + 77 + 10 = 93 → Correct.

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12.) -5 + 5x = 10x + 4 - 6x

Simplify right: 10x - 6x = 4x → so:
-5 + 5x = 4x + 4

Subtract 4x:
-5 + x = 4

Add 5:
x = 9

✔ Check: -5 + 45 = 40; 40 + 4 - 54? Wait — let’s recheck:

Right side: 10×9 + 4 - 6×9 = 90 + 4 - 54 = 40 → yes. Left: -5 + 45 = 40 → Correct.

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13.) x - 9 - 5x = 2 - 5x

Combine left: -4x - 9 = 2 - 5x

Add 5x:
x - 9 = 2

Add 9:
x = 11

✔ Check: 11 - 9 - 55 = -53; 2 - 55 = -53 → Correct.

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14.) 38 + 12x = 64 - x

Add x:
38 + 13x = 64

Subtract 38:
13x = 26

x = 2

✔ Check: 38 + 24 = 62; 64 - 2 = 62 → Correct.

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15.) 3x - 10 = 4x - 8

Subtract 3x:
-10 = x - 8

Add 8:
-2 = x

x = -2

✔ Check: 3×(-2)-10 = -6-10=-16; 4×(-2)-8=-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: -12 + 2 = -10; 2×(-12) + 14 = -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.) 2
15.) -2
16.) -12