1. **State the problem:** Solve the equation $$-10x + 2x = -72$$ for $x$. 2. **Combine like terms:** On the left side, combine $-10x$ and $2x$: $$-10x + 2x = (-10 + 2)x = -8x$$ So the equation becomes: $$-8x = -72$$ 3. **Isolate $x$:** Divide both sides by $-8$ to solve for $x$: $$\frac{-8x}{\cancel{-8}} = \frac{-72}{\cancel{-8}}$$ $$x = 9$$ 4. **Conclusion:** The solution to the equation is $x = 9$. The value $x = -9$ is not a solution because substituting it back does not satisfy the equation. **Final answer:** $x = 9$