We are tasked with solving the equation:

\[
\frac{9 - 4r}{8} = 3 + \frac{r}{3}
\]

### Step 1: Eliminate the Denominators
Multiply both sides of the equation by 24 (the least common denominator of 8 and 3) to eliminate the fractions:

\[
24 \times \left(\frac{9 - 4r}{8}\right) = 24 \times \left(3 + \frac{r}{3}\right)
\]

Simplifying each term:

\[
3(9 - 4r) = 24(3) + 8r
\]

This gives:

\[
3(9 - 4r) = 72 + 8r
\]

### Step 2: Distribute and Simplify
Distribute the 3 on the left-hand side:

\[
27 - 12r = 72 + 8r
\]

### Step 3: Move all terms with \(r\) to one side
Move all terms involving \(r\) to one side and constants to the other side:

\[
27 - 72 = 8r + 12r
\]

This simplifies to:

\[
-45 = 20r
\]

### Step 4: Solve for \(r\)
Now, divide both sides by 20:

\[
r = \frac{-45}{20}
\]

Simplify the fraction:

\[
r = -\frac{9}{4}
\]

Thus, the solution is:

\[
r = -\frac{9}{4}
\]

Would you like more details or have any questions?

### Related questions:
1. How do you check if your solution to an equation is correct?
2. What happens if the variables are on both sides of the equation?
3. How do you solve a system of equations with fractions?
4. What are common mistakes when solving equations with fractions?
5. How do you simplify complex fractions?

### Tip:
Always simplify fractions as much as possible to make further calculations easier.

Learn how to solve the linear equation 9 - 4r/8 = 3 + r/3 with step-by-step guidance. This problem demonstrates how to eliminate fractions, apply the distributive property, and solve for variables. Suitable for students in Grades 8-10.

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