1. **State the problem:** Solve the equation $$\frac{1}{2} + x - \frac{3}{4} = -0.75$$ for $x$. 2. **Rewrite the equation:** Convert decimals to fractions for consistency. Note that $-0.75 = -\frac{3}{4}$. 3. **Substitute:** The equation becomes $$\frac{1}{2} + x - \frac{3}{4} = -\frac{3}{4}$$. 4. **Isolate $x$:** Add $\frac{3}{4}$ to both sides to cancel the $-\frac{3}{4}$ on the left: $$\frac{1}{2} + x - \frac{3}{4} + \frac{3}{4} = -\frac{3}{4} + \frac{3}{4}$$ 5. **Simplify:** The $-\frac{3}{4}$ and $+\frac{3}{4}$ cancel out: $$\frac{1}{2} + x = 0$$ 6. **Solve for $x$:** Subtract $\frac{1}{2}$ from both sides: $$x = 0 - \frac{1}{2}$$ 7. **Final answer:** $$x = -\frac{1}{2}$$