1. **State the problem:** Solve the inequality $$8x + 120 < 4x - 64$$ for $x$. 2. **Isolate the variable terms:** Subtract $4x$ from both sides to get all $x$ terms on one side. $$8x + 120 - 4x < 4x - 64 - 4x$$ 3. **Simplify:** $$\cancel{8x} + 120 - \cancel{4x} < \cancel{4x} - 64 - \cancel{4x}$$ which simplifies to $$4x + 120 < -64$$ 4. **Isolate $x$:** Subtract 120 from both sides. $$4x + 120 - 120 < -64 - 120$$ $$4x < -184$$ 5. **Solve for $x$:** Divide both sides by 4. $$\frac{4x}{\cancel{4}} < \frac{-184}{\cancel{4}}$$ $$x < -46$$ **Final answer:** $$x < -46$$