1. **State the problem:** Solve the inequality $-x - \frac{3}{4} > 7$ for $x$. 2. **Write the inequality:** $$-x - \frac{3}{4} > 7$$ 3. **Isolate the term with $x$:** Add $\frac{3}{4}$ to both sides: $$-x - \frac{3}{4} + \frac{3}{4} > 7 + \frac{3}{4}$$ $$-x > 7 + \frac{3}{4}$$ 4. **Simplify the right side:** $$7 + \frac{3}{4} = \frac{28}{4} + \frac{3}{4} = \frac{31}{4}$$ So, $$-x > \frac{31}{4}$$ 5. **Divide both sides by $-1$ to solve for $x$:** Remember, dividing by a negative number reverses the inequality sign. $$\frac{-x}{-1} < \frac{31}{4} \times \frac{-1}{-1}$$ $$\cancel{-}x \times \cancel{-1} < -\frac{31}{4}$$ $$x < -\frac{31}{4}$$ 6. **Final answer:** $$x < -\frac{31}{4}$$ This means $x$ must be less than $-7.75$ to satisfy the inequality.