1. **State the problem:** Solve the inequality $2(x+3)<14$ for $x$. 2. **Use the distributive property:** Multiply 2 by each term inside the parentheses. $$2(x+3) = 2 \times x + 2 \times 3 = 2x + 6$$ So the inequality becomes: $$2x + 6 < 14$$ 3. **Isolate the variable term:** Subtract 6 from both sides. $$2x + 6 - 6 < 14 - 6$$ $$2x < 8$$ 4. **Divide both sides by 2 to solve for $x$:** $$\frac{\cancel{2}x}{\cancel{2}} < \frac{8}{2}$$ $$x < 4$$ 5. **Final answer:** The solution to the inequality is: $$x < 4$$ This means any value of $x$ less than 4 satisfies the original inequality.