The problem asks us to find the value of $x$ for which the expression

$\frac{9 - 4x}{5} = 3$

To solve this, we start by multiplying both sides by 5 to eliminate the denominator:

$9 - 4x = 3 \times 5$

Simplifying the right side:

$9 - 4x = 15$

Next, we isolate $x$ by first subtracting 9 from both sides:

$-4x = 15 - 9$

$-4x = 6$

Now, divide both sides by -4 to solve for $x$:

$x = \frac{6}{-4}$

$x = -\frac{3}{2}$

So, the value of $x$ that satisfies the equation is:

$\boxed{-\frac{3}{2}}$

Would you like further details or have any other questions? Here are some related questions that might interest you:

1. How do you solve linear equations with fractions?
2. What are other methods to solve equations involving fractions?
3. Can we graph the equation to verify the solution?
4. How do we solve equations with variables on both sides?
5. What are common mistakes to avoid when solving equations with fractions?

Tip: When solving equations with fractions, it's often helpful to first eliminate the fractions by multiplying both sides by the least common denominator.