1. **State the problem:** Solve the inequality $$4 > -8x$$. 2. **Recall the rule for inequalities:** When dividing or multiplying both sides of an inequality by a negative number, the inequality sign must be reversed. 3. **Isolate $x$:** Divide both sides by $-8$ (a negative number), so we must reverse the inequality sign: $$4 > -8x$$ Divide both sides by $\cancel{-8}$ with reversal: $$\frac{4}{\cancel{-8}} < x$$ 4. **Simplify the fraction:** $$\frac{4}{-8} = -\frac{1}{2}$$ So, $$x > -\frac{1}{2}$$ 5. **Interpretation:** The solution is all $x$ values greater than $-\frac{1}{2}$. **Final answer:** $$x > -\frac{1}{2}$$