1. **State the problem:** Solve the proportion $$\frac{30}{40} = \frac{18}{x+18}$$ for $x$. 2. **Use the cross-multiplication formula for proportions:** If $$\frac{a}{b} = \frac{c}{d}$$ then $$a \times d = b \times c$$. 3. **Apply cross multiplication:** $$30 \times (x + 18) = 40 \times 18$$ 4. **Expand the left side:** $$30x + 30 \times 18 = 720$$ $$30x + 540 = 720$$ 5. **Isolate $x$ by subtracting 540 from both sides:** $$30x + \cancel{540} - \cancel{540} = 720 - 540$$ $$30x = 180$$ 6. **Divide both sides by 30 to solve for $x$:** $$\frac{30x}{\cancel{30}} = \frac{180}{\cancel{30}}$$ $$x = 6$$ **Final answer:** $$x = 6$$