1. **State the problem:** Solve the inequality $2(x - 1) < 6 - x$. 2. **Apply the distributive property:** $$2(x - 1) = 2x - 2$$ So the inequality becomes: $$2x - 2 < 6 - x$$ 3. **Add $x$ to both sides to collect $x$ terms on the left:** $$2x - 2 + x < 6 - x + x$$ $$3x - 2 < 6$$ 4. **Add 2 to both sides to isolate the term with $x$:** $$3x - 2 + 2 < 6 + 2$$ $$3x < 8$$ 5. **Divide both sides by 3 to solve for $x$:** $$\frac{\cancel{3}x}{\cancel{3}} < \frac{8}{3}$$ $$x < \frac{8}{3}$$ **Final answer:** $$x < \frac{8}{3}$$ This means all values of $x$ less than $\frac{8}{3}$ satisfy the inequality.