Let's solve the inequality step by step.
Question 1: Which step is needed to solve the inequality?
The inequality to solve is:
\[ 59w \geq 8 \]
To solve for \( w \), we need to isolate \( w \) on one side. The best way to do that here is to divide both sides of the inequality by 59:
\[ w \geq \frac{8}{59} \]
So the correct response from the options is:
Divide 59 on both sides of the inequality.
Question 2: Determine the solution to the inequality.
Now let's calculate:
\[ \frac{8}{59} \approx 0.135593 \]
This does not match any of the options perfectly, but we can express \( \frac{8}{59} \) in decimal or fraction terms.
To check options:
- w ≥ 1425 - doesn't match.
- w is greater than or equal to 14 and 2 fifths - doesn't match.
- w ≥ 859 - doesn't match.
- w ≥ 749 - doesn't match.
The options provided do not show \( w \geq \frac{8}{59} \). If \( \frac{8}{59} \) were expressed as a decimal, it could be approximated but not directly represented in fractional terms provided.
Assuming we take \( \frac{8}{59} \) as the main value, none of the choices align well with it. However, from none of the given answers directly corresponding, the closest could be interpreted as a misalignment on representation.
Question 3: How should the solution of the inequality be graphed?
Because the inequality is \( \geq \), we have a closed circle on the graph, representing that \( w \) can equal \( \frac{8}{59} \) and include all values greater than that.
Thus, the correct choice would be:
Closed circle, shade right.
To summarize:
- Divide 59 on both sides of the inequality.
- None of the given exact responses match \( \frac{8}{59} \).
- Closed circle, shade right.