1. **State the problem:** Make $x$ the subject of the formula given by $$9y = \frac{5 - 2x}{2}$$ 2. **Start by eliminating the denominator:** Multiply both sides by 2 to get rid of the fraction: $$2 \times 9y = 2 \times \frac{5 - 2x}{2}$$ $$18y = 5 - 2x$$ 3. **Isolate the term with $x$:** Subtract 5 from both sides: $$18y - 5 = 5 - 2x - 5$$ $$18y - 5 = -2x$$ 4. **Make $x$ the subject:** Divide both sides by $-2$: $$\frac{18y - 5}{-2} = \frac{-2x}{-2}$$ $$\cancel{\frac{18y - 5}{\cancel{-2}}} = \cancel{\frac{-2x}{\cancel{-2}}}$$ $$x = \frac{5 - 18y}{2}$$ 5. **Final answer:** $$x = \frac{5 - 18y}{2}$$ This means $x$ is expressed in terms of $y$ by rearranging the original formula and carefully handling the negative coefficient.