1. **State the problem:** Solve for $x$ in the equation $$\frac{3x + 4y}{5} = z.$$ 2. **Isolate the term with $x$:** Multiply both sides by 5 to eliminate the denominator: $$3x + 4y = 5z.$$ 3. **Solve for $x$:** Subtract $4y$ from both sides: $$3x = 5z - 4y.$$ 4. **Divide both sides by 3 to isolate $x$:** $$x = \frac{5z - 4y}{3}.$$ 5. **Interpretation:** The placeholders in the numerator correspond to $z$ and $y$ respectively, so the expression is $$x = \frac{5z - 4y}{3}.$$ This is the solution for $x$ in terms of $y$ and $z$.