Question
What steps would you follow to graph the inequality statement?
-4 ≥ -w
place an open circle on 4 and shade to the left
place a closed circle on 4 and shade to the right
place a closed circle on -4 and shade to the right
place an open circle on -4 and shade to the left
-4 ≥ -w
place an open circle on 4 and shade to the left
place a closed circle on 4 and shade to the right
place a closed circle on -4 and shade to the right
place an open circle on -4 and shade to the left
Answers
GPT-4o mini
To graph the inequality \(-4 \geq -w\), follow these steps:
1. **Rewrite the inequality**: To make it easier to graph, you can rearrange the inequality. It can be rewritten as \(w \geq 4\) by multiplying both sides by \(-1\) and reversing the inequality sign.
2. **Identify the critical point**: The critical point from the rewritten inequality \(w \geq 4\) is \(4\).
3. **Determine the type of circle**: Since the inequality is "greater than or equal to" (\(\geq\)), you will use a **closed circle** on \(4\).
4. **Shade the appropriate region**: Since \(w\) is greater than or equal to \(4\), you will shade to the **right** of the closed circle at \(4\).
Thus the correct answer is:
- **place a closed circle on 4 and shade to the right.**
1. **Rewrite the inequality**: To make it easier to graph, you can rearrange the inequality. It can be rewritten as \(w \geq 4\) by multiplying both sides by \(-1\) and reversing the inequality sign.
2. **Identify the critical point**: The critical point from the rewritten inequality \(w \geq 4\) is \(4\).
3. **Determine the type of circle**: Since the inequality is "greater than or equal to" (\(\geq\)), you will use a **closed circle** on \(4\).
4. **Shade the appropriate region**: Since \(w\) is greater than or equal to \(4\), you will shade to the **right** of the closed circle at \(4\).
Thus the correct answer is:
- **place a closed circle on 4 and shade to the right.**