1. **State the problem:** Solve the equation $$4x - 4 = 5(x - 9)$$. 2. **Apply the distributive property:** Expand the right side: $$4x - 4 = 5x - 45$$ 3. **Isolate variable terms on one side:** Subtract $5x$ from both sides: $$4x - 5x - 4 = 5x - 5x - 45$$ $$\cancel{4x} - \cancel{5x} - 4 = \cancel{5x} - \cancel{5x} - 45$$ $$-x - 4 = -45$$ 4. **Isolate the variable term:** Add 4 to both sides: $$-x - 4 + 4 = -45 + 4$$ $$-x = -41$$ 5. **Solve for $x$:** Multiply both sides by $-1$: $$-1 \times -x = -1 \times -41$$ $$x = 41$$ **Final answer:** $x = 41$