1. **State the problem:** Solve the linear equation $$5x - 23 = 10(x - 1)$$ for $x$ and express the answer as a decimal. 2. **Expand the right side:** Use the distributive property to expand $$10(x - 1)$$: $$5x - 23 = 10x - 10$$ 3. **Bring all terms involving $x$ to one side:** Subtract $10x$ from both sides: $$5x - 10x - 23 = 10x - 10x - 10$$ $$\cancel{5x} - \cancel{10x} - 23 = \cancel{10x} - \cancel{10x} - 10$$ $$-5x - 23 = -10$$ 4. **Isolate the $x$ term:** Add 23 to both sides: $$-5x - 23 + 23 = -10 + 23$$ $$-5x = 13$$ 5. **Solve for $x$:** Divide both sides by $-5$: $$x = \frac{13}{-5}$$ $$x = -\frac{13}{5}$$ 6. **Convert to decimal:** $$x = -2.6$$ **Final answer:** $$x = -2.6$$