Answer: -9/2

Multiply both sides by $28$: $7(2x + 9) = 4(2x + 9)$. Subtract $4(2x + 9)$ from both sides: $3(2x + 9) = 0$. So $2x + 9 = 0$ and $x = -\frac{9}{2}$, or $-4.5$.

Dividing both sides by $2x + 9$ gives $\frac{1}{4} = \frac{1}{7}$, which suggests there is no solution, but that step isn't allowed when $2x + 9 = 0$.