1. **State the problem:** Solve the equation $$4(x + 4) = x + 1$$. 2. **Apply the distributive property:** Multiply 4 by each term inside the parentheses. $$4x + 16 = x + 1$$ 3. **Isolate variable terms on one side:** Subtract $$x$$ from both sides. $$4x - \cancel{x} + 16 = \cancel{x} + 1 - x$$ $$4x - x + 16 = 1$$ 4. **Simplify the left side:** $$3x + 16 = 1$$ 5. **Isolate the variable term:** Subtract 16 from both sides. $$3x + 16 - 16 = 1 - 16$$ $$3x = -15$$ 6. **Solve for $$x$$:** Divide both sides by 3. $$\frac{3x}{\cancel{3}} = \frac{-15}{\cancel{3}}$$ $$x = -5$$ **Final answer:** $$x = -5$$