Math Ged Practice Test Worksheets - Free Printable

Let’s solve each problem one by one.

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Problem 1: 14.13 = x - 4.25

We want to find x.
Add 4.25 to both sides:
14.13 + 4.25 = x
x = 18.38

✔ Check: 18.38 - 4.25 = 14.13 → Correct.

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Problem 2: 14.1 + x = 43.9

Subtract 14.1 from both sides:
x = 43.9 - 14.1
x = 29.8

✔ Check: 14.1 + 29.8 = 43.9 → Correct.

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Problem 3: 4x - 10 = x - 7

Get all x terms on one side, constants on the other.
Subtract x from both sides:
3x - 10 = -7
Add 10 to both sides:
3x = 3
Divide by 3:
x = 1

✔ Check: 4(1) - 10 = -6; 1 - 7 = -6 → Correct.

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Problem 4: 2 - x = 5x - 10

Move x terms to one side, constants to the other.
Add x to both sides:
2 = 6x - 10
Add 10 to both sides:
12 = 6x
Divide by 6:
x = 2

✔ Check: 2 - 2 = 0; 5(2) - 10 = 0 → Correct.

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Problem 5: 2 + x = -5x - 22

Add 5x to both sides:
2 + 6x = -22
Subtract 2:
6x = -24
Divide by 6:
x = -4

✔ Check: 2 + (-4) = -2; -5(-4) - 22 = 20 - 22 = -2 → Correct.

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Problem 6: 2 + 4x = 2x + 20

Subtract 2x from both sides:
2 + 2x = 20
Subtract 2:
2x = 18
Divide by 2:
x = 9

✔ Check: 2 + 4(9) = 38; 2(9) + 20 = 38 → Correct.

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Problem 7: -1 + 4x = 6x - 7

Subtract 4x from both sides:
-1 = 2x - 7
Add 7:
6 = 2x
Divide by 2:
x = 3

✔ Check: -1 + 4(3) = 11; 6(3) - 7 = 11 → Correct.

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Problem 8: (42x³)/(2x)

Simplify: divide coefficients and subtract exponents.
42 ÷ 2 = 21
x³ ÷ x = x²
Answer: 21x²

✔ Check: 21x² * 2x = 42x³ → Correct.

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Problem 9: (52x²)/(2x)

52 ÷ 2 = 26
x² ÷ x = x
Answer: 26x

✔ Check: 26x * 2x = 52x² → Correct.

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Problem 10: (x² + 7x + 6)/(x + 1)

Factor numerator:
x² + 7x + 6 = (x + 1)(x + 6)
So: [(x + 1)(x + 6)] / (x + 1) = x + 6 (as long as x ≠ -1)

Answer: x + 6

✔ Check: (x+6)(x+1) = x² + 7x + 6 → Correct.

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Problem 11: (x + 2)/(x² + 9x + 18)

Factor denominator:
x² + 9x + 18 = (x + 3)(x + 6)
Numerator is x + 2 — no common factors.

Answer: (x + 2)/[(x + 3)(x + 6)]

✔ No simplification possible — correct as is.

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Problem 12: (x² + 8x + 15)/(x² + 6x + 8)

Factor numerator: x² + 8x + 15 = (x + 3)(x + 5)
Factor denominator: x² + 6x + 8 = (x + 2)(x + 4)
No common factors.

Answer: [(x + 3)(x + 5)] / [(x + 2)(x + 4)]

✔ Can’t simplify further — correct.

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Final Answer:
1. x = 18.38
2. x = 29.8
3. x = 1
4. x = 2
5. x = -4
6. x = 9
7. x = 3
8. 21x²
9. 26x
10. x + 6
11. (x + 2)/[(x + 3)(x + 6)]
12. [(x + 3)(x + 5)] / [(x + 2)(x + 4)]