1. **State the problem:** Solve the system of inequalities: $$-1 - x \leq 0$$ and $$-2x - 1 \geq -3$$ 2. **Solve the first inequality:** $$-1 - x \leq 0$$ Add 1 to both sides: $$-x \leq 1$$ Multiply both sides by $-1$ and reverse the inequality sign: $$x \geq -1$$ 3. **Solve the second inequality:** $$-2x - 1 \geq -3$$ Add 1 to both sides: $$-2x \geq -2$$ Divide both sides by $-2$ and reverse the inequality sign: $$x \leq 1$$ 4. **Combine the solutions:** From the first inequality, $x \geq -1$. From the second inequality, $x \leq 1$. Therefore, the solution set is: $$-1 \leq x \leq 1$$ This means $x$ can be any number between $-1$ and $1$, inclusive.