To solve the inequality \( \frac{5}{9}w \geq 8 \), you need to isolate \( w \). Here's how you can do that step by step:
- Multiply both sides by the reciprocal of \( \frac{5}{9} \), which is \( \frac{9}{5} \). This step helps eliminate the fraction and isolate \( w \).
So the step you would take is:
\[ w \geq 8 \cdot \frac{9}{5} \]
Calculating that gives:
\[ w \geq \frac{72}{5} \]
Thus, the main step needed to solve the inequality is multiplying both sides by \( \frac{9}{5} \).