1. **State the problem:** Solve the two-step equation $$4z + 1 = 41$$ for the variable $z$. 2. **Formula and rules:** To solve two-step equations, we first undo addition or subtraction, then undo multiplication or division. 3. **Step 1: Subtract 1 from both sides** to isolate the term with $z$: $$4z + 1 - 1 = 41 - 1$$ $$4z = 40$$ 4. **Step 2: Divide both sides by 4** to solve for $z$: $$\frac{\cancel{4}z}{\cancel{4}} = \frac{40}{4}$$ $$z = 10$$ 5. **Final answer:** $z = 10$. This means when $z$ is 10, the original equation holds true.