1. **State the problem:** Solve the inequality $$-1 - (-4x + \frac{5}{2}) - 3x \leq -\frac{1}{2}x$$. 2. **Distribute the negative sign inside the parentheses:** $$-1 + 4x - \frac{5}{2} - 3x \leq -\frac{1}{2}x$$ 3. **Combine like terms on the left side:** $$-1 - \frac{5}{2} + 4x - 3x \leq -\frac{1}{2}x$$ 4. **Simplify constants:** $$-1 - \frac{5}{2} = -\frac{2}{2} - \frac{5}{2} = -\frac{7}{2}$$ So the inequality becomes: $$-\frac{7}{2} + (4x - 3x) \leq -\frac{1}{2}x$$ 5. **Simplify the x terms:** $$-\frac{7}{2} + x \leq -\frac{1}{2}x$$ 6. **Add $$\frac{1}{2}x$$ to both sides to get all x terms on the left:** $$-\frac{7}{2} + x + \frac{1}{2}x \leq -\frac{1}{2}x + \frac{1}{2}x$$ Intermediate step showing cancellation: $$-\frac{7}{2} + \cancel{x} + \frac{1}{2}x \leq \cancel{-\frac{1}{2}x} + 0$$ 7. **Combine x terms:** $$-\frac{7}{2} + \frac{3}{2}x \leq 0$$ 8. **Add $$\frac{7}{2}$$ to both sides:** $$-\frac{7}{2} + \frac{3}{2}x + \frac{7}{2} \leq 0 + \frac{7}{2}$$ Intermediate step showing cancellation: $$\cancel{-\frac{7}{2}} + \frac{3}{2}x + \cancel{\frac{7}{2}} \leq \frac{7}{2}$$ 9. **Simplify:** $$\frac{3}{2}x \leq \frac{7}{2}$$ 10. **Divide both sides by $$\frac{3}{2}$$ (which is positive, so inequality direction stays the same):** $$x \leq \frac{7}{2} \div \frac{3}{2} = \frac{7}{2} \times \frac{2}{3} = \frac{7}{3}$$ **Final answer:** $$x \leq \frac{7}{3}$$