https://file.aiquickdraw.com/mathbot/file/172652680358566qp0jh0.jpg

Let's solve the equation shown in the image:

\[
8x - 6 = \frac{2}{3}(6x + 15)
\]

### Step 1: Distribute the fraction on the right-hand side
We distribute \(\frac{2}{3}\) across the terms inside the parentheses:

\[
\frac{2}{3}(6x + 15) = \frac{2}{3} \times 6x + \frac{2}{3} \times 15 = 4x + 10
\]

Now, the equation becomes:

\[
8x - 6 = 4x + 10
\]

### Step 2: Move all terms involving \(x\) to one side
We subtract \(4x\) from both sides:

\[
8x - 4x - 6 = 10
\]
\[
4x - 6 = 10
\]

### Step 3: Isolate \(x\)
Add 6 to both sides:

\[
4x = 16
\]

Now, divide both sides by 4:

\[
x = \frac{16}{4} = 4
\]

### Final answer:
\[
x = 4
\]

Let me know if you'd like further details or clarification!

### Related Questions:
1. How do you distribute fractions over parentheses?
2. What would change if the coefficient on the right-hand side was different, e.g., \(\frac{3}{4}\)?
3. How do you verify if a solution is correct by substituting back into the equation?
4. What if the equation had multiple fractions?
5. How do you solve for \(x\) if the equation involves square roots?

### Tip:
Always check your solution by plugging the value of \(x\) back into the original equation to confirm it holds true!

Solve the equation 8x - 6 = (2/3)(6x + 15).

Learn how to solve the linear equation 8x - 6 = (2/3)(6x + 15) with a step-by-step solution. This problem covers key algebraic concepts, including distribution of fractions and solving for x. Suitable for students in Grades 8-10.

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