1. **State the problem:** Solve the equation $$\frac{1}{2}(x - 3) = 24$$ for $$x$$. 2. **Understand the operations:** The equation represents two operations applied to $$x$$: first subtract 3, then multiply the result by $$\frac{1}{2}$$. 3. **Isolate the expression:** To solve for $$x$$, undo the operations in reverse order. 4. **Undo multiplication by $$\frac{1}{2}$$:** Multiply both sides by 2. $$\cancel{\frac{1}{2}}(x - 3) \times 2 = 24 \times 2$$ which simplifies to $$x - 3 = 48$$ 5. **Undo subtraction of 3:** Add 3 to both sides. $$x - 3 + 3 = 48 + 3$$ which simplifies to $$x = 51$$ 6. **Final answer:** $$x = 51$$ This means when $$x = 51$$, the original equation holds true.