1. **State the problem:** Solve the linear equation $$4 - 3(x + 1) = 2x - 4$$. 2. **Use the distributive property:** Expand terms with parentheses. $$4 - 3x - 3 = 2x - 4$$ 3. **Simplify the left side:** Combine like terms. $$1 - 3x = 2x - 4$$ 4. **Isolate variable terms on one side:** Add $3x$ to both sides. $$1 - \cancel{3x} + 3x = 2x + 3x - 4$$ $$1 = 5x - 4$$ 5. **Isolate constant terms on the other side:** Add $4$ to both sides. $$1 + 4 = 5x - 4 + 4$$ $$5 = 5x$$ 6. **Solve for $x$ by dividing both sides by $5$:** $$\frac{5}{\cancel{5}} = \frac{5x}{\cancel{5}}$$ $$1 = x$$ **Final answer:** $$x = 1$$