Question
Consider the inequality.
59w≥8
Which step is needed to solve this inequality?
(1 point)
Responses
Add 59
to both sides of the inequality.
Add 5 ninths to both sides of the inequality.
Subtract 59
to both sides of the inequality.
Subtract 5 ninths to both sides of the inequality.
Multiply 59
on both sides of the inequality.
Multiply 5 ninths on both sides of the inequality.
Divide 59
on both sides of the inequality.
Divide 5 ninths on both sides of the inequality.
Question 2
Determine the solution to the inequality.(1 point)
Responses
w≥859
w is greater than or equal to 8 and 5 ninths
w≥749
w is greater than or equal to 7 and 4 ninths
w≥445
w is greater than or equal to 4 and 4 fifths
w≥1425
w is greater than or equal to 14 and 2 fifths
Question 3
How should the solution of the inequality be graphed?(1 point)
Responses
Open circle, shade right
Open circle, shade right
Open circle, shade left
Open circle, shade left
Closed circle, shade right
Closed circle, shade right
Closed circle, shade left
Closed circle, shade left
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59w≥8
Which step is needed to solve this inequality?
(1 point)
Responses
Add 59
to both sides of the inequality.
Add 5 ninths to both sides of the inequality.
Subtract 59
to both sides of the inequality.
Subtract 5 ninths to both sides of the inequality.
Multiply 59
on both sides of the inequality.
Multiply 5 ninths on both sides of the inequality.
Divide 59
on both sides of the inequality.
Divide 5 ninths on both sides of the inequality.
Question 2
Determine the solution to the inequality.(1 point)
Responses
w≥859
w is greater than or equal to 8 and 5 ninths
w≥749
w is greater than or equal to 7 and 4 ninths
w≥445
w is greater than or equal to 4 and 4 fifths
w≥1425
w is greater than or equal to 14 and 2 fifths
Question 3
How should the solution of the inequality be graphed?(1 point)
Responses
Open circle, shade right
Open circle, shade right
Open circle, shade left
Open circle, shade left
Closed circle, shade right
Closed circle, shade right
Closed circle, shade left
Closed circle, shade left
Skip to navigation
Answers
GPT-4o mini
Let's solve each part of your questions step-by-step.
### Question 1: Which step is needed to solve the inequality \( 59w \geq 8 \)?
To isolate \( w \), you would need to divide both sides of the inequality by \( 59 \).
**Correct response:**
- **Divide 59 on both sides of the inequality.**
### Question 2: Determine the solution to the inequality \( 59w \geq 8 \).
After dividing both sides of the inequality by \( 59 \):
\[
w \geq \frac{8}{59}
\]
Now, we can calculate that:
\[
\frac{8}{59} \approx 0.135593
\]
This value doesn't match any of the options provided. The numerical expressions in the responses you provided (like \( 8 \frac{5}{9} \) or \( 7 \frac{4}{9} \)) don’t seem relevant to the simple fraction result we found. The provided options may need to be checked against the original format of fractions.
However, based on the calculations:
- Suggesting that \( w = \frac{8}{59} \) means the answer choice doesn't directly match.
So, the closest logical answer from the provided choices would typically be labeled:
- \( w \geq 8 \frac{5}{9} \) would not accurately represent \( \frac{8}{59} \) and none of the remaining alternatives seem to match after the calculations.
### Question 3: How should the solution of the inequality be graphed?
Since the inequality is \( \geq \), it includes \( \frac{8}{59} \) and represents all values greater than that.
Hence, you would graph this as:
- **Closed circle at \( 8/59 \) and shade to the right.**
**Correct response:**
- **Closed circle, shade right.**
In summary:
1. Divide \( 59 \) on both sides of the inequality.
2. The answer needs checking against options provided, as none reflect the output correctly.
3. Graph with a closed circle at \( \frac{8}{59} \) and shade to the right.
### Question 1: Which step is needed to solve the inequality \( 59w \geq 8 \)?
To isolate \( w \), you would need to divide both sides of the inequality by \( 59 \).
**Correct response:**
- **Divide 59 on both sides of the inequality.**
### Question 2: Determine the solution to the inequality \( 59w \geq 8 \).
After dividing both sides of the inequality by \( 59 \):
\[
w \geq \frac{8}{59}
\]
Now, we can calculate that:
\[
\frac{8}{59} \approx 0.135593
\]
This value doesn't match any of the options provided. The numerical expressions in the responses you provided (like \( 8 \frac{5}{9} \) or \( 7 \frac{4}{9} \)) don’t seem relevant to the simple fraction result we found. The provided options may need to be checked against the original format of fractions.
However, based on the calculations:
- Suggesting that \( w = \frac{8}{59} \) means the answer choice doesn't directly match.
So, the closest logical answer from the provided choices would typically be labeled:
- \( w \geq 8 \frac{5}{9} \) would not accurately represent \( \frac{8}{59} \) and none of the remaining alternatives seem to match after the calculations.
### Question 3: How should the solution of the inequality be graphed?
Since the inequality is \( \geq \), it includes \( \frac{8}{59} \) and represents all values greater than that.
Hence, you would graph this as:
- **Closed circle at \( 8/59 \) and shade to the right.**
**Correct response:**
- **Closed circle, shade right.**
In summary:
1. Divide \( 59 \) on both sides of the inequality.
2. The answer needs checking against options provided, as none reflect the output correctly.
3. Graph with a closed circle at \( \frac{8}{59} \) and shade to the right.