1. **State the problem:** Solve the linear equation $9 - 5x = 19$ for $x$. 2. **Formula and rules:** The equation is in the form $a - bx = c$. To solve for $x$, first isolate the term with $x$ by subtracting $a$ from both sides, then divide both sides by $-b$. 3. **Step 1: Subtract 9 from both sides** $$9 - 5x - 9 = 19 - 9$$ $$-5x = 10$$ 4. **Step 2: Divide both sides by $-5$ to isolate $x$** $$\frac{-5x}{\cancel{-5}} = \frac{10}{\cancel{-5}}$$ $$x = -2$$ 5. **Final answer:** The solution is $x = -2$.