To solve the inequality \( \frac{5}{9}w \geq 8 \), let's address each question sequentially.
Question 1: Which step is needed to solve this inequality?
To isolate \( w \), you need to divide both sides by \( \frac{5}{9} \). Therefore, the correct option is:
- Divide \( \frac{5}{9} \) on both sides of the inequality.
Question 2: Determine the solution to the inequality.
If we divide both sides of the inequality \( \frac{5}{9}w \geq 8 \) by \( \frac{5}{9} \), we also need to multiply the right side by the reciprocal of \( \frac{5}{9} \):
\[ w \geq 8 \cdot \frac{9}{5} \]
Calculating \( 8 \cdot \frac{9}{5} \):
\[ 8 \cdot \frac{9}{5} = \frac{72}{5} = 14.4 \]
This can be expressed as \( 14 \frac{2}{5} \).
So, the correct answer is:
- w ≥ 14 2/5 (w is greater than or equal to 14 and 2 fifths)
Question 3: How should the solution of the inequality be graphed?
Since the inequality is \( w \geq 14 \frac{2}{5} \), it includes the endpoint, so we use a closed circle at \( 14 \frac{2}{5} \) and shade to the right (indicating all values greater than or equal to this point).
Therefore, the correct option is:
- Closed circle, shade right.
If you have any more questions or need further assistance, feel free to ask!