1. **State the problem:** Solve the equation $20 + x : (-3) = 18 \frac{1}{2}$ for $x$. 2. **Rewrite the equation:** The colon $:$ means division, so the equation is $$20 + \frac{x}{-3} = 18 \frac{1}{2}$$ Convert the mixed number to an improper fraction: $$18 \frac{1}{2} = \frac{37}{2}$$ So the equation becomes $$20 + \frac{x}{-3} = \frac{37}{2}$$ 3. **Isolate the term with $x$:** Subtract 20 from both sides: $$\frac{x}{-3} = \frac{37}{2} - 20$$ Convert 20 to fraction with denominator 2: $$20 = \frac{40}{2}$$ So $$\frac{x}{-3} = \frac{37}{2} - \frac{40}{2} = \frac{37 - 40}{2} = \frac{-3}{2}$$ 4. **Solve for $x$:** Multiply both sides by $-3$: $$x = -3 \times \frac{-3}{2}$$ Show cancellation step: $$x = \cancel{-3} \times \frac{\cancel{-3}}{2} = \frac{9}{2}$$ 5. **Final answer:** $$x = \frac{9}{2} = 4 \frac{1}{2}$$ So, the solution is $x = 4 \frac{1}{2}$.