https://file.aiquickdraw.com/mathbot/file/1726867435035xg43x864.jpg

The equation extracted from the image is:

\[
2(4x + 2) = 4x - 12(x - 1)
\]

Let's solve it step by step.

### Step 1: Expand both sides
On the left side:
\[
2(4x + 2) = 8x + 4
\]

On the right side:
\[
4x - 12(x - 1) = 4x - 12x + 12 = -8x + 12
\]

So, the equation becomes:
\[
8x + 4 = -8x + 12
\]

### Step 2: Combine like terms
Move all terms involving \(x\) to one side and constant terms to the other side:
\[
8x + 8x = 12 - 4
\]
\[
16x = 8
\]

### Step 3: Solve for \(x\)
\[
x = \frac{8}{16} = \frac{1}{2}
\]

Thus, the solution is \(x = \frac{1}{2}\).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you handle similar equations with fractions?
2. What if we need to solve quadratic equations instead?
3. How do you check if a solution satisfies the original equation?
4. Can you explain how to solve inequalities involving similar steps?
5. What are the best methods to factor complex expressions?

**Tip:** Always simplify both sides of the equation before solving for \(x\), as this reduces errors and makes the process easier.

This detailed guide shows how to solve the linear equation 2(4x + 2) = 4x - 12(x - 1). Learn the steps using the distributive property, combining like terms, and solving for x. Suitable for students in Grades 7-9.

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