Free 9th Grade Math Worksheets—Printable w/ Answers — Mashup Math - Free Printable

Problem: Solving Two-Sided Algebraic Equations

The task is to solve each of the given two-sided algebraic equations. Below, I will solve each equation step by step.

---

#### 1. \( x + 142 = 16x + 7 \)

1. Subtract \( x \) from both sides:
\[
142 = 15x + 7
\]
2. Subtract 7 from both sides:
\[
135 = 15x
\]
3. Divide both sides by 15:
\[
x = 9
\]

Solution: \( x = 9 \)

---

#### 2. \( 8x = 2x - 6 \)

1. Subtract \( 2x \) from both sides:
\[
6x = -6
\]
2. Divide both sides by 6:
\[
x = -1
\]

Solution: \( x = -1 \)

---

#### 3. \( 1 + 9x = 7 + 8x \)

1. Subtract \( 8x \) from both sides:
\[
1 + x = 7
\]
2. Subtract 1 from both sides:
\[
x = 6
\]

Solution: \( x = 6 \)

---

#### 4. \( -8x + 8 = 10 + 5 - 9x \)

1. Simplify the right-hand side:
\[
-8x + 8 = 15 - 9x
\]
2. Add \( 9x \) to both sides:
\[
x + 8 = 15
\]
3. Subtract 8 from both sides:
\[
x = 7
\]

Solution: \( x = 7 \)

---

#### 5. \( 7x + 2 = -10x + 2 \)

1. Add \( 10x \) to both sides:
\[
17x + 2 = 2
\]
2. Subtract 2 from both sides:
\[
17x = 0
\]
3. Divide both sides by 17:
\[
x = 0
\]

Solution: \( x = 0 \)

---

#### 6. \( 55 - x = 2x + 13 \)

1. Add \( x \) to both sides:
\[
55 = 3x + 13
\]
2. Subtract 13 from both sides:
\[
42 = 3x
\]
3. Divide both sides by 3:
\[
x = 14
\]

Solution: \( x = 14 \)

---

#### 7. \( -3x - 4x = -8x + 1 \)

1. Combine like terms on the left-hand side:
\[
-7x = -8x + 1
\]
2. Add \( 8x \) to both sides:
\[
x = 1
\]

Solution: \( x = 1 \)

---

#### 8. \( 5 - 5x + 6 = 4 - 4x \)

1. Simplify both sides:
\[
11 - 5x = 4 - 4x
\]
2. Add \( 5x \) to both sides:
\[
11 = 4 + x
\]
3. Subtract 4 from both sides:
\[
7 = x
\]

Solution: \( x = 7 \)

---

#### 9. \( 7x - 5 = 9x + 9 \)

1. Subtract \( 7x \) from both sides:
\[
-5 = 2x + 9
\]
2. Subtract 9 from both sides:
\[
-14 = 2x
\]
3. Divide both sides by 2:
\[
x = -7
\]

Solution: \( x = -7 \)

---

#### 10. \( -20 - 8x = 5x - 7 \)

1. Add \( 8x \) to both sides:
\[
-20 = 13x - 7
\]
2. Add 7 to both sides:
\[
-13 = 13x
\]
3. Divide both sides by 13:
\[
x = -1
\]

Solution: \( x = -1 \)

---

#### 11. \( 100 - x = 6 + 11x + 10 \)

1. Simplify the right-hand side:
\[
100 - x = 16 + 11x
\]
2. Add \( x \) to both sides:
\[
100 = 16 + 12x
\]
3. Subtract 16 from both sides:
\[
84 = 12x
\]
4. Divide both sides by 12:
\[
x = 7
\]

Solution: \( x = 7 \)

---

#### 12. \( -5 + 5x = 10x + 4 - 6x \)

1. Simplify the right-hand side:
\[
-5 + 5x = 4x + 4
\]
2. Subtract \( 4x \) from both sides:
\[
-5 + x = 4
\]
3. Add 5 to both sides:
\[
x = 9
\]

Solution: \( x = 9 \)

---

#### 13. \( x - 9 - 5x = 2 - 5x \)

1. Simplify the left-hand side:
\[
-4x - 9 = 2 - 5x
\]
2. Add \( 5x \) to both sides:
\[
x - 9 = 2
\]
3. Add 9 to both sides:
\[
x = 11
\]

Solution: \( x = 11 \)

---

#### 14. \( 38 + 12x = 64 - x \)

1. Add \( x \) to both sides:
\[
38 + 13x = 64
\]
2. Subtract 38 from both sides:
\[
13x = 26
\]
3. Divide both sides by 13:
\[
x = 2
\]

Solution: \( x = 2 \)

---

#### 15. \( 3x - 10 = 4x - 8 \)

1. Subtract \( 3x \) from both sides:
\[
-10 = x - 8
\]
2. Add 8 to both sides:
\[
-2 = x
\]

Solution: \( x = -2 \)

---

#### 16. \( x + 2 = 2x + 14 \)

1. Subtract \( x \) from both sides:
\[
2 = x + 14
\]
2. Subtract 14 from both sides:
\[
x = -12
\]

Solution: \( x = -12 \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & x = 9 \\
2. & x = -1 \\
3. & x = 6 \\
4. & x = 7 \\
5. & x = 0 \\
6. & x = 14 \\
7. & x = 1 \\
8. & x = 7 \\
9. & x = -7 \\
10. & x = -1 \\
11. & x = 7 \\
12. & x = 9 \\
13. & x = 11 \\
14. & x = 2 \\
15. & x = -2 \\
16. & x = -12 \\
\end{array}
}
\]