Math Ged Practice Test Worksheets - Free Printable

Let's solve the equations step by step. I'll provide detailed explanations for each problem.

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Part 1: Solving Linear Equations (Problems 1–7)

#### Problem 1:
\[ 14.13 = x - 4.25 \]

1. Add 4.25 to both sides:
\[
14.13 + 4.25 = x
\]
2. Simplify:
\[
x = 18.38
\]

Answer:
\[
\boxed{18.38}
\]

---

#### Problem 2:
\[ 14.1 + x = 43.9 \]

1. Subtract 14.1 from both sides:
\[
x = 43.9 - 14.1
\]
2. Simplify:
\[
x = 29.8
\]

Answer:
\[
\boxed{29.8}
\]

---

#### Problem 3:
\[ 4x - 10 = x - 7 \]

1. Subtract \( x \) from both sides:
\[
4x - x - 10 = -7
\]
2. Simplify:
\[
3x - 10 = -7
\]
3. Add 10 to both sides:
\[
3x = 3
\]
4. Divide by 3:
\[
x = 1
\]

Answer:
\[
\boxed{1}
\]

---

#### Problem 4:
\[ 2 - x = 5x - 10 \]

1. Add \( x \) to both sides:
\[
2 = 6x - 10
\]
2. Add 10 to both sides:
\[
12 = 6x
\]
3. Divide by 6:
\[
x = 2
\]

Answer:
\[
\boxed{2}
\]

---

#### Problem 5:
\[ 2 + x = -5x - 22 \]

1. Add \( 5x \) to both sides:
\[
2 + 6x = -22
\]
2. Subtract 2 from both sides:
\[
6x = -24
\]
3. Divide by 6:
\[
x = -4
\]

Answer:
\[
\boxed{-4}
\]

---

#### Problem 6:
\[ 2 + 4x = 2x + 20 \]

1. Subtract \( 2x \) from both sides:
\[
2 + 2x = 20
\]
2. Subtract 2 from both sides:
\[
2x = 18
\]
3. Divide by 2:
\[
x = 9
\]

Answer:
\[
\boxed{9}
\]

---

#### Problem 7:
\[ -1 + 4x = 6x - 7 \]

1. Subtract \( 4x \) from both sides:
\[
-1 = 2x - 7
\]
2. Add 7 to both sides:
\[
6 = 2x
\]
3. Divide by 2:
\[
x = 3
\]

Answer:
\[
\boxed{3}
\]

---

Part 2: Simplifying Rational Expressions (Problems 8–12)

#### Problem 8:
\[ \frac{42x^3}{2x} \]

1. Simplify the fraction by canceling common factors:
\[
\frac{42x^3}{2x} = \frac{42}{2} \cdot \frac{x^3}{x} = 21x^2
\]

Answer:
\[
\boxed{21x^2}
\]

---

#### Problem 9:
\[ \frac{52x^2}{2x} \]

1. Simplify the fraction by canceling common factors:
\[
\frac{52x^2}{2x} = \frac{52}{2} \cdot \frac{x^2}{x} = 26x
\]

Answer:
\[
\boxed{26x}
\]

---

#### Problem 10:
\[ \frac{x^2 + 7x + 6}{x + 1} \]

1. Factor the numerator:
\[
x^2 + 7x + 6 = (x + 1)(x + 6)
\]
2. Rewrite the expression:
\[
\frac{(x + 1)(x + 6)}{x + 1}
\]
3. Cancel the common factor \( x + 1 \) (assuming \( x \neq -1 \)):
\[
x + 6
\]

Answer:
\[
\boxed{x + 6}
\]

---

#### Problem 11:
\[ \frac{x + 2}{x^2 + 9x + 18} \]

1. Factor the denominator:
\[
x^2 + 9x + 18 = (x + 3)(x + 6)
\]
2. Rewrite the expression:
\[
\frac{x + 2}{(x + 3)(x + 6)}
\]
3. The numerator \( x + 2 \) cannot be factored further, and it does not cancel with the denominator. So the expression is already in its simplest form.

Answer:
\[
\boxed{\frac{x + 2}{(x + 3)(x + 6)}}
\]

---

#### Problem 12:
\[ \frac{x^2 + 8x + 15}{x^2 + 6x + 8} \]

1. Factor the numerator:
\[
x^2 + 8x + 15 = (x + 3)(x + 5)
\]
2. Factor the denominator:
\[
x^2 + 6x + 8 = (x + 2)(x + 4)
\]
3. Rewrite the expression:
\[
\frac{(x + 3)(x + 5)}{(x + 2)(x + 4)}
\]
4. The numerator and denominator do not have any common factors, so the expression is already in its simplest form.

Answer:
\[
\boxed{\frac{(x + 3)(x + 5)}{(x + 2)(x + 4)}}
\]

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Final Answers:

1. \(\boxed{18.38}\)
2. \(\boxed{29.8}\)
3. \(\boxed{1}\)
4. \(\boxed{2}\)
5. \(\boxed{-4}\)
6. \(\boxed{9}\)
7. \(\boxed{3}\)
8. \(\boxed{21x^2}\)
9. \(\boxed{26x}\)
10. \(\boxed{x + 6}\)
11. \(\boxed{\frac{x + 2}{(x + 3)(x + 6)}}\)
12. \(\boxed{\frac{(x + 3)(x + 5)}{(x + 2)(x + 4)}}\)