1. **State the problem:** Solve the equation $$80x - 160x + 26.67(x - 1) = 0$$. 2. **Combine like terms:** First, combine the terms involving $x$ on the left side. $$80x - 160x = -80x$$ So the equation becomes: $$-80x + 26.67(x - 1) = 0$$ 3. **Distribute the 26.67:** $$-80x + 26.67x - 26.67 = 0$$ 4. **Combine like terms again:** $$(-80x + 26.67x) - 26.67 = 0$$ $$-53.33x - 26.67 = 0$$ 5. **Isolate the variable term:** $$-53.33x = 26.67$$ 6. **Divide both sides by -53.33:** $$x = \frac{26.67}{\cancel{-53.33}}\cancel{-1} = -\frac{26.67}{53.33}$$ 7. **Simplify the fraction:** $$x = -0.5$$ **Final answer:** $$x = -0.5$$