1. **State the problem:** Solve the equation $-24 = -2(x + 19)$ for $x$. 2. **Use the distributive property:** Multiply $-2$ by each term inside the parentheses. $$-24 = -2 \times x + (-2) \times 19$$ $$-24 = -2x - 38$$ 3. **Isolate the term with $x$:** Add $38$ to both sides to move constants to the left. $$-24 + 38 = -2x - 38 + 38$$ $$14 = -2x$$ 4. **Solve for $x$:** Divide both sides by $-2$. $$\frac{14}{\cancel{-2}} = \frac{-2x}{\cancel{-2}}$$ $$x = -7$$ 5. **Final answer:** $x = -7$. This means the value of $x$ that satisfies the equation is $-7$.