Question: Solve for $x$:
$-2x + 0.5(3x + 10) = -1.1 - (5.5x + 5)$
1. **State the problem:** Solve the equation $$-2x + 0.5(3x + 10) = -1.1 - (5.5x + 5)$$ for $x$.
2. **Distribute and simplify both sides:**
$$-2x + 0.5 \times 3x + 0.5 \times 10 = -1.1 - 5.5x - 5$$
which simplifies to
$$-2x + 1.5x + 5 = -1.1 - 5.5x - 5$$
3. **Combine like terms on each side:**
$$(-2x + 1.5x) + 5 = (-1.1 - 5) - 5.5x$$
$$-0.5x + 5 = -6.1 - 5.5x$$
4. **Add $5.5x$ to both sides to get all $x$ terms on one side:**
$$-0.5x + 5.5x + 5 = -6.1 - 5.5x + 5.5x$$
$$5x + 5 = -6.1$$
5. **Subtract 5 from both sides:**
$$5x + \cancel{5} - \cancel{5} = -6.1 - 5$$
$$5x = -11.1$$
6. **Divide both sides by 5 to solve for $x$:**
$$x = \frac{-11.1}{5}$$
7. **Calculate the division:**
$$x = -2.22$$
**Final answer:** $$x = -2.22$$