1. **State the problem:** Solve the equation $3 - 5x = -42$ for $x$. 2. **Isolate the term with $x$:** Subtract 3 from both sides to get the term with $x$ alone. $$3 - 5x - 3 = -42 - 3$$ $$\cancel{3} - 5x - \cancel{3} = -42 - 3$$ $$-5x = -45$$ 3. **Solve for $x$:** Divide both sides by $-5$ to isolate $x$. $$\frac{-5x}{-5} = \frac{-45}{-5}$$ $$\cancel{-5}x / \cancel{-5} = \cancel{-45} / \cancel{-5}$$ $$x = 9$$ 4. **Final answer:** $x = 9$. This means that when $x$ is 9, the original equation holds true.