1. **State the problem:** Solve the inequality $$4 > -3x + 1$$. 2. **Rewrite the inequality:** We want to isolate $x$ on one side. 3. **Subtract 1 from both sides:** $$4 - 1 > -3x + 1 - 1$$ $$3 > -3x$$ 4. **Divide both sides by -3:** When dividing by a negative number, the inequality sign reverses. $$\frac{3}{\cancel{-3}} < \frac{-3x}{\cancel{-3}}$$ $$-1 < x$$ 5. **Rewrite the solution:** $$x > -1$$ **Answer:** The solution to the inequality is $$x > -1$$, meaning all values of $x$ greater than $-1$ satisfy the inequality.