1. **State the problem:** We need to determine which values of $x$ satisfy the inequality $$4(2 - x) > -2x - 3(4x + 1).$$ 2. **Expand both sides:** $$4 \times 2 - 4 \times x > -2x - 3 \times 4x - 3 \times 1$$ $$8 - 4x > -2x - 12x - 3$$ 3. **Simplify the right side:** $$8 - 4x > -14x - 3$$ 4. **Add $14x$ to both sides to collect $x$ terms on the left:** $$8 - 4x + 14x > -14x - 3 + 14x$$ $$8 + 10x > -3$$ 5. **Subtract 8 from both sides:** $$8 + 10x - 8 > -3 - 8$$ $$10x > -11$$ 6. **Divide both sides by 10:** $$\frac{\cancel{10}x}{\cancel{10}} > \frac{-11}{10}$$ $$x > -1.1$$ 7. **Interpretation:** The solution to the inequality is all $x$ values greater than $-1.1$. 8. **Check each given value:** - $x = -1.1$: Not greater than $-1.1$, so **no**. - $x = -2.2$: Less than $-1.1$, so **no**. - $x = 0$: Greater than $-1.1$, so **yes**. - $x = -10$: Less than $-1.1$, so **no**. - $x = 10$: Greater than $-1.1$, so **yes**. **Final answer:** The values $x = 0$ and $x = 10$ satisfy the inequality.