9Th Grade Algebra Worksheets — db-excel.com - Free Printable

The image contains a worksheet titled "Solving Linear Equations (C)" with several sections of problems. Below, I will solve one problem from each section to demonstrate the process of solving linear equations. If you need solutions for specific problems or all problems, please let me know!

---

Section A: Basic Linear Equations

#### Problem 1: \( 4x + 10 = 30 \)
1. Subtract 10 from both sides:
\[
4x + 10 - 10 = 30 - 10
\]
\[
4x = 20
\]
2. Divide both sides by 4:
\[
\frac{4x}{4} = \frac{20}{4}
\]
\[
x = 5
\]

Solution: \( x = 5 \)

---

Section B: Equations with Fractions

#### Problem 1: \( \frac{x}{2} + 11 = 19 \)
1. Subtract 11 from both sides:
\[
\frac{x}{2} + 11 - 11 = 19 - 11
\]
\[
\frac{x}{2} = 8
\]
2. Multiply both sides by 2:
\[
2 \cdot \frac{x}{2} = 8 \cdot 2
\]
\[
x = 16
\]

Solution: \( x = 16 \)

---

Section C: Distributive Property

#### Problem 1: \( 3(x + 2) = 15 \)
1. Distribute the 3:
\[
3x + 6 = 15
\]
2. Subtract 6 from both sides:
\[
3x + 6 - 6 = 15 - 6
\]
\[
3x = 9
\]
3. Divide both sides by 3:
\[
\frac{3x}{3} = \frac{9}{3}
\]
\[
x = 3
\]

Solution: \( x = 3 \)

---

Section D: Variables on Both Sides

#### Problem 1: \( x + 8 = 3x \)
1. Subtract \( x \) from both sides:
\[
x + 8 - x = 3x - x
\]
\[
8 = 2x
\]
2. Divide both sides by 2:
\[
\frac{8}{2} = \frac{2x}{2}
\]
\[
x = 4
\]

Solution: \( x = 4 \)

---

Section E: More Complex Equations

#### Problem 1: \( 9x + 2 = 4x + 12 \)
1. Subtract \( 4x \) from both sides:
\[
9x + 2 - 4x = 4x + 12 - 4x
\]
\[
5x + 2 = 12
\]
2. Subtract 2 from both sides:
\[
5x + 2 - 2 = 12 - 2
\]
\[
5x = 10
\]
3. Divide both sides by 5:
\[
\frac{5x}{5} = \frac{10}{5}
\]
\[
x = 2
\]

Solution: \( x = 2 \)

---

Final Answers for Demonstrated Problems

\[
\boxed{
\begin{aligned}
&\text{Section A: } x = 5 \\
&\text{Section B: } x = 16 \\
&\text{Section C: } x = 3 \\
&\text{Section D: } x = 4 \\
&\text{Section E: } x = 2
\end{aligned}
}
\]

If you need solutions for other problems, please specify!