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The image contains five linear equations to solve. Here are the equations extracted from the image:

1. \(8(2x) = 4(2x + 4)\)
2. \(7x + 5x = 9x - 9\)
3. \(10(x + 2) - 3(x - 2) - 2(x - 2) = 0\)
4. \(12x - 10 = 48\)
5. \(4(x + 2) = 2 - 6x\)

I will solve each equation step-by-step.

### 1. Solve: \(8(2x) = 4(2x + 4)\)

First, expand both sides:
\[
8 \cdot 2x = 4 \cdot (2x + 4)
\]
\[
16x = 8x + 16
\]

Rearrange to isolate \(x\):
\[
16x - 8x = 16
\]
\[
8x = 16
\]
\[
x = 2
\]

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

Combine like terms on the left side:
\[
12x = 9x - 9
\]

Rearrange to isolate \(x\):
\[
12x - 9x = -9
\]
\[
3x = -9
\]
\[
x = -3
\]

### 3. Solve: \(10(x + 2) - 3(x - 2) - 2(x - 2) = 0\)

Expand each term:
\[
10x + 20 - 3x + 6 - 2x + 4 = 0
\]
Combine like terms:
\[
(10x - 3x - 2x) + (20 + 6 + 4) = 0
\]
\[
5x + 30 = 0
\]

Rearrange to isolate \(x\):
\[
5x = -30
\]
\[
x = -6
\]

### 4. Solve: \(12x - 10 = 48\)

Rearrange to isolate \(x\):
\[
12x = 48 + 10
\]
\[
12x = 58
\]
\[
x = \frac{58}{12} = \frac{29}{6} \approx 4.83
\]

### 5. Solve: \(4(x + 2) = 2 - 6x\)

Expand the left side:
\[
4x + 8 = 2 - 6x
\]

Rearrange to isolate \(x\):
\[
4x + 6x = 2 - 8
\]
\[
10x = -6
\]
\[
x = -\frac{3}{5} = -0.6
\]

### Summary of Solutions:
1. \(x = 2\)
2. \(x = -3\)
3. \(x = -6\)
4. \(x = \frac{29}{6}\)
5. \(x = -0.6\)

Would you like more details on any specific equation, or do you have any questions? 

#### Related Questions:
1. How can we check if the solutions are correct for each equation?
2. What are the different methods to solve linear equations?
3. Can we solve these equations graphically? How?
4. How does one handle equations with variables on both sides?
5. What is the significance of checking solutions in linear equations?

#### Tip:
Always check your solution by substituting the value of \(x\) back into the original equation to verify that it satisfies both sides of the equation.

Solve the linear equations in one variable below and check your solution.

Learn how to solve linear equations such as 8(2x) = 4(2x + 4) with detailed steps. This guide covers key algebraic concepts like combining like terms, isolating the variable, and applying the distributive property. Suitable for students in Grades 7-9.

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