2. \( \frac{2}{3} w-3 \leq 7 \)

To solve the inequality \( \frac{2}{3} w - 3 \leq 7 \), you first add 3 to both sides, giving you \( \frac{2}{3} w \leq 10 \). Next, multiply both sides by \( \frac{3}{2} \) to isolate \( w \), resulting in \( w \leq 15 \). Thus, \( w \) can take any value less than or equal to 15. Always remember to flip the inequality sign only when multiplying or dividing by a negative number! A common mistake is forgetting this rule when working with inequalities, leading to incorrect solutions. When in doubt, check your work by plugging values back into the original inequality!