1. **State the problem:** Solve the equation $x - 1 = 0.4x - 2.5$ for $x$. 2. **Write down the equation:** $$x - 1 = 0.4x - 2.5$$ 3. **Isolate the variable terms on one side:** Subtract $0.4x$ from both sides: $$x - 0.4x - 1 = 0.4x - 0.4x - 2.5$$ $$x - 0.4x - 1 = -2.5$$ 4. **Simplify the left side:** $$\cancel{x} - \cancel{0.4x} = 0.6x$$ So, $$0.6x - 1 = -2.5$$ 5. **Add 1 to both sides to isolate the term with $x$:** $$0.6x - 1 + 1 = -2.5 + 1$$ $$0.6x = -1.5$$ 6. **Divide both sides by 0.6 to solve for $x$:** $$x = \frac{-1.5}{0.6}$$ Show cancellation: $$x = \frac{-1.5}{0.6} = \frac{-\cancel{1.5}}{\cancel{0.6}} \times \frac{10}{10} = \frac{-15}{6}$$ 7. **Simplify the fraction:** $$x = \frac{-15}{6} = \frac{-5 \times 3}{2 \times 3} = \frac{-5}{2} = -2.5$$ **Final answer:** $$x = -2.5$$