We are given the equation:

$\frac{3x + 8}{3} = \frac{5}{4}x + 5$

Step 1: Eliminate the denominator on the left side

Multiply both sides of the equation by 3 to eliminate the denominator on the left side:

$3x + 8 = 3 \left( \frac{5}{4}x + 5 \right)$

Step 2: Distribute the 3 on the right side

$3x + 8 = \frac{15}{4}x + 15$

Step 3: Multiply through by 4 to eliminate the fraction

Multiply both sides by 4 to eliminate the fraction:

$4(3x + 8) = 4\left( \frac{15}{4}x + 15 \right)$

This simplifies to:

$12x + 32 = 15x + 60$

Step 4: Rearrange the equation to isolate $x$

Subtract $12x$ from both sides:

$32 = 3x + 60$

Now subtract 60 from both sides:

$-28 = 3x$

Step 5: Solve for $x$

Divide both sides by 3:

$x = \frac{-28}{3}$

Thus, $x = -\frac{28}{3}$.

Would you like more details, or do you have any questions about the process?

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Here are 5 questions related to this:

1. How do you handle equations with fractions and variables?
2. What methods can be used to simplify linear equations?
3. How do you know when to multiply both sides of an equation?
4. Why is it important to isolate the variable on one side of the equation?
5. How can you check if your solution is correct?

Tip: Always double-check your work by substituting the solution back into the original equation.