1. **State the problem:** Solve the equation $-x + 5 = 9x$ for $x$. 2. **Formula and rules:** To solve linear equations, we isolate the variable on one side by performing inverse operations. 3. **Step 1:** Add $x$ to both sides to move all $x$ terms to one side: $$-x + 5 + x = 9x + x$$ which simplifies to $$5 = 10x$$ 4. **Step 2:** Divide both sides by 10 to solve for $x$: $$\frac{5}{\cancel{10}} = \frac{10x}{\cancel{10}}$$ which simplifies to $$x = \frac{5}{10}$$ 5. **Step 3:** Simplify the fraction: $$x = \frac{1}{2}$$ **Final answer:** $$x = \frac{1}{2}$$