1. **State the problem:** Solve the linear equation $-3x + 3 = 4 - 3$ for $x$. 2. **Simplify the right side:** $$4 - 3 = 1$$ So the equation becomes: $$-3x + 3 = 1$$ 3. **Isolate the term with $x$:** Subtract 3 from both sides: $$-3x + 3 - 3 = 1 - 3$$ $$-3x = -2$$ 4. **Divide both sides by $-3$ to solve for $x$:** $$x = \frac{-2}{-3}$$ Show the cancellation: $$x = \frac{\cancel{-2}}{\cancel{-3}} = \frac{2}{3}$$ 5. **Final answer:** $$x = \frac{2}{3}$$ This means the value of $x$ that satisfies the equation is $\frac{2}{3}$.