To solve the equation \( \frac{4}{3}(x + 8) = 9 \), follow these steps:

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 3 to eliminate the denominator on the left-hand side:

\[
3 \times \frac{4}{3}(x + 8) = 3 \times 9
\]

This simplifies to:

\[
4(x + 8) = 27
\]

### Step 2: Distribute the 4
Now, distribute the 4 on the left-hand side:

\[
4x + 32 = 27
\]

### Step 3: Isolate \( x \)
Subtract 32 from both sides:

\[
4x = 27 - 32
\]

\[
4x = -5
\]

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

\[
x = \frac{-5}{4}
\]

Thus, the solution is:

\[
x = -\frac{5}{4} \quad \text{or} \quad x = -1.25
\]

Would you like further details or explanations on any of the steps?

### Related Questions:
1. How do you solve equations with fractions in general?
2. What is the process for solving multi-step equations?
3. Can you explain how to simplify expressions with variables?
4. How do you check if your solution is correct by substituting it back into the equation?
5. What happens if there are variables on both sides of the equation?

### Tip:
Always aim to eliminate fractions early in an equation to simplify your work!

Learn how to solve the linear equation 4/3(x + 8) = 9 with this detailed step-by-step guide. This problem covers key algebraic concepts, such as eliminating fractions, using the distributive property, and isolating the variable. Suitable for students in Grades 6-8.

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