Question: Solve for $x$.
$3 - \frac{9}{2} = \frac{2x - 5}{18}$
1. **State the problem:** Solve the equation $$3 - \frac{9}{2} = \frac{2x - 5}{18}$$ for $x$.
2. **Rewrite the left side:** Convert $3$ to a fraction with denominator $2$ to combine terms:
$$3 = \frac{6}{2}$$
So,
$$\frac{6}{2} - \frac{9}{2} = \frac{6 - 9}{2} = \frac{-3}{2}$$
3. **Rewrite the equation:**
$$\frac{-3}{2} = \frac{2x - 5}{18}$$
4. **Cross multiply to clear denominators:**
$$-3 \times 18 = 2 \times (2x - 5)$$
5. **Calculate left side:**
$$-54 = 2(2x - 5)$$
6. **Distribute right side:**
$$-54 = 4x - 10$$
7. **Isolate $x$:**
Add $10$ to both sides:
$$-54 + 10 = 4x$$
$$-44 = 4x$$
8. **Divide both sides by $4$:**
$$x = \frac{-44}{4}$$
Show cancellation:
$$x = \frac{\cancel{44}}{\cancel{4}} \times \frac{-1}{1} = -11$$
9. **Final answer:**
$$\boxed{x = -11}$$