Let's break down the steps to solve the given inequality \( \frac{5}{9}w \geq 8 \).
Question 1
To isolate \( w \) in the inequality \( \frac{5}{9}w \geq 8 \), we need to eliminate the fraction. The correct step is to multiply by the reciprocal of \( \frac{5}{9} \), which is \( \frac{9}{5} \).
So the correct choice is:
Multiply \( 5/9 \) on both sides of the inequality.
Question 2
To solve for \( w \), we multiply both sides of the inequality by \( \frac{9}{5} \):
\[ w \geq 8 \cdot \frac{9}{5} \]
Calculating that:
\[ w \geq \frac{72}{5} \]
To convert \( \frac{72}{5} \) to a mixed number, we divide 72 by 5:
\[ 72 ÷ 5 = 14 \text{ remainder } 2 \quad \Rightarrow \quad 14 \frac{2}{5} \]
Thus, the solution is:
w ≥ 14 and 2/5
Question 3
Since the inequality is \( w \geq 14 \frac{2}{5} \), this means that \( w \) is greater than or equal to a specific value. Therefore, we should graph this with a closed circle at \( 14 \frac{2}{5} \) and shade to the right of that point to indicate that all values greater than or equal to this point satisfy the inequality.
Thus, the correct choice is:
Closed circle, shade right.
Summary of Answers:
- Multiply \( 5/9 \) on both sides of the inequality.
- w ≥ 14 and 2/5
- Closed circle, shade right.