https://file.aiquickdraw.com/mathbot/file/1727191834530wqcupk43.jpg

Let's solve the equation shown in the image:

\[
3(2x - 8) = 2(4 - x)
\]

### Step 1: Expand both sides
First, distribute the constants on both sides:

\[
3 \times (2x - 8) = 6x - 24
\]
\[
2 \times (4 - x) = 8 - 2x
\]

Now the equation becomes:

\[
6x - 24 = 8 - 2x
\]

### Step 2: Collect like terms
Move the terms involving \( x \) to one side and the constants to the other:

\[
6x + 2x = 8 + 24
\]

This simplifies to:

\[
8x = 32
\]

### Step 3: Solve for \( x \)
Now divide both sides by 8:

\[
x = \frac{32}{8} = 4
\]

Thus, the solution is \( x = 4 \).

Would you like more details or further explanation? Here are some related questions:

1. How do you check if a solution is correct by substituting it back into the original equation?
2. What are the common steps in solving linear equations with brackets?
3. How does distributing constants in front of parentheses work?
4. Can this type of equation have multiple solutions, and why not in this case?
5. What happens if you simplify both sides before solving?

**Tip:** Always simplify both sides of the equation before attempting to move terms across the equal sign.

Learn how to solve the linear equation 3(2x - 8) = 2(4 - x) with a step-by-step breakdown. This guide covers key algebra concepts such as distribution and solving for x, suitable for students in Grades 6-8.

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