1. **State the problem:** Solve the inequality $4 > -8x$ for $x$. 2. **Write the inequality:** $$4 > -8x$$ 3. **Isolate $x$:** To solve for $x$, divide both sides by $-8$. Remember, dividing by a negative number reverses the inequality sign. 4. **Divide both sides:** $$\frac{4}{\cancel{-8}} \; \cancel{>} \; \frac{-8x}{\cancel{-8}}$$ This becomes: $$\frac{4}{-8} < x$$ 5. **Simplify the fraction:** $$-\frac{1}{2} < x$$ 6. **Rewrite the solution:** $$x > -\frac{1}{2}$$ **Explanation:** When dividing by a negative number, the inequality sign flips. So the solution is all $x$ values greater than $-\frac{1}{2}$. **Final answer:** $$x > -\frac{1}{2}$$