Let's solve the equation:

\[
11 = \frac{2}{3}(8x + 12)
\]

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 3 to get rid of the denominator:

\[
3 \times 11 = 3 \times \frac{2}{3}(8x + 12)
\]

This simplifies to:

\[
33 = 2(8x + 12)
\]

### Step 2: Distribute the 2
Distribute the 2 to both terms inside the parentheses:

\[
33 = 16x + 24
\]

### Step 3: Isolate the variable term
Subtract 24 from both sides to move the constant to the other side:

\[
33 - 24 = 16x
\]

This simplifies to:

\[
9 = 16x
\]

### Step 4: Solve for \( x \)
Divide both sides by 16 to solve for \( x \):

\[
x = \frac{9}{16}
\]

Thus, the solution is:

\[
x = \frac{9}{16}
\]

Would you like more details or have any questions?

Here are 5 related questions you could explore:
1. How would the solution change if the equation was \(11 = \frac{2}{5}(8x + 12)\)?
2. What happens when you multiply both sides of an equation by a fraction?
3. How do you solve similar equations with larger numbers or more complex fractions?
4. Can you solve for \( x \) in an equation where both sides contain variables and fractions?
5. What are common mistakes when solving fractional equations?

**Tip:** Always check your solution by substituting \( x \) back into the original equation to verify it.

This guide walks through solving the linear equation 11 = 2/3(8x + 12), covering concepts like fraction elimination, the distributive property, and isolating variables. Suitable for students in Grades 7-9 looking to strengthen their algebra skills.

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