1. **State the problem:** Solve the equation $x - 63 + x + 24 = 32$ for $x$. 2. **Combine like terms:** Group the $x$ terms and the constants separately. $$x + x - 63 + 24 = 32$$ $$2x - 39 = 32$$ 3. **Isolate the variable term:** Add 39 to both sides to move the constant term. $$2x - 39 + 39 = 32 + 39$$ $$2x = 71$$ 4. **Solve for $x$:** Divide both sides by 2. $$\frac{\cancel{2}x}{\cancel{2}} = \frac{71}{2}$$ $$x = \frac{71}{2}$$ 5. **Final answer:** $$x = 35.5$$