https://file.aiquickdraw.com/mathbot/file/1726243688679kpyo4ny5.jpg

The equation in the image is:

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

### To solve for \( x \):

1. **Multiply both sides by 4 to eliminate the denominator**:

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

\[
3(x + 8) = 36
\]

2. **Divide both sides by 3 to isolate the \( x + 8 \) term**:

\[
x + 8 = \frac{36}{3}
\]

\[
x + 8 = 12
\]

3. **Subtract 8 from both sides** to solve for \( x \):

\[
x = 12 - 8
\]

\[
x = 4
\]

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

Would you like any further details or have any questions?

Here are five related questions for further practice:
1. Solve \( \frac{2}{3}(x - 5) = 10 \).
2. Solve \( \frac{5}{6}(2x + 3) = 15 \).
3. What happens if \( \frac{3}{4}(x + 8) = 12 \)? How does that change \( x \)?
4. Solve \( \frac{7}{5}(x - 9) = 14 \).
5. Solve \( 2x + 3 = 9 \).

**Tip**: Always remember to first eliminate any fractions by multiplying both sides of the equation by the denominator!

Learn how to solve the linear equation 3/4(x + 8) = 9 step-by-step. This problem covers key algebraic concepts, including working with fractions and isolating variables. Suitable for students in Grades 6-8.

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