1. **State the problem:** Solve the equation $8x - 40 = 20x - 4$ for $x$. 2. **Write the formula and rules:** To solve linear equations, we isolate the variable $x$ by performing the same operations on both sides. 3. **Step 1: Move all $x$ terms to one side and constants to the other:** $$8x - 40 = 20x - 4$$ Subtract $8x$ from both sides: $$8x - 40 - 8x = 20x - 4 - 8x$$ Simplifies to: $$-40 = 12x - 4$$ 4. **Step 2: Move constants to the other side:** Add $4$ to both sides: $$-40 + 4 = 12x - 4 + 4$$ Simplifies to: $$-36 = 12x$$ 5. **Step 3: Solve for $x$ by dividing both sides by $12$:** $$x = \frac{-36}{12}$$ Show cancellation: $$x = \frac{\cancel{12} \times (-3)}{\cancel{12}}$$ Simplifies to: $$x = -3$$ 6. **Final answer:** $$\boxed{-3}$$