Question
Consider the inequality.
5/9w≥8
Which step is needed to solve this inequality?
(1 point)
Responses
Add 5/9
to both sides of the inequality.
Add 5 ninths to both sides of the inequality.
Subtract 5/9
to both sides of the inequality.
Subtract 5 ninths to both sides of the inequality.
Multiply 5/9
on both sides of the inequality.
Multiply 5 ninths on both sides of the inequality.
Divide 5/9
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≥8 5/9
w is greater than or equal to 8 and 5 ninths
w≥7 4/9
w is greater than or equal to 7 and 4 ninths
w≥4 4/5
w is greater than or equal to 4 and 4 fifths
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?(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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5/9w≥8
Which step is needed to solve this inequality?
(1 point)
Responses
Add 5/9
to both sides of the inequality.
Add 5 ninths to both sides of the inequality.
Subtract 5/9
to both sides of the inequality.
Subtract 5 ninths to both sides of the inequality.
Multiply 5/9
on both sides of the inequality.
Multiply 5 ninths on both sides of the inequality.
Divide 5/9
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≥8 5/9
w is greater than or equal to 8 and 5 ninths
w≥7 4/9
w is greater than or equal to 7 and 4 ninths
w≥4 4/5
w is greater than or equal to 4 and 4 fifths
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?(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 go through the questions step by step.
### Question 1:
The inequality given is:
\[
\frac{5}{9}w \geq 8
\]
To solve for \( w \), we need to isolate it on one side. The term \(\frac{5}{9}\) is multiplied by \( w \). Thus, to eliminate \(\frac{5}{9}\), we need to **divide both sides by \(\frac{5}{9}\)**.
So the correct response is:
- **Divide \(\frac{5}{9}\) on both sides of the inequality.**
### Question 2:
Next, we can solve the inequality. Dividing both sides by \(\frac{5}{9}\) gives us:
\[
w \geq 8 \div \frac{5}{9}
\]
Dividing by a fraction is the same as multiplying by its reciprocal, so we can rewrite this as:
\[
w \geq 8 \times \frac{9}{5}
\]
Calculating that:
\[
8 \times \frac{9}{5} = \frac{72}{5} = 14.4
\]
So, \( \frac{72}{5} = 14 \frac{2}{5} \). Thus,
\[
w \geq 14 \frac{2}{5}
\]
So the correct response is:
- **w ≥ 14 2/5 (or w is greater than or equal to 14 and 2 fifths)**
### Question 3:
Since the solution involves \( w \geq 14 \frac{2}{5} \), we will use a closed circle at \( 14 \frac{2}{5} \) to denote that it includes this value (since it is "greater than or equal to"), and we shade to the right to indicate all values greater than \( 14 \frac{2}{5} \).
Thus, the correct response is:
- **Closed circle, shade right.**
To sum up the answers:
1. Divide \(\frac{5}{9}\) on both sides of the inequality.
2. w ≥ 14 2/5.
3. Closed circle, shade right.
### Question 1:
The inequality given is:
\[
\frac{5}{9}w \geq 8
\]
To solve for \( w \), we need to isolate it on one side. The term \(\frac{5}{9}\) is multiplied by \( w \). Thus, to eliminate \(\frac{5}{9}\), we need to **divide both sides by \(\frac{5}{9}\)**.
So the correct response is:
- **Divide \(\frac{5}{9}\) on both sides of the inequality.**
### Question 2:
Next, we can solve the inequality. Dividing both sides by \(\frac{5}{9}\) gives us:
\[
w \geq 8 \div \frac{5}{9}
\]
Dividing by a fraction is the same as multiplying by its reciprocal, so we can rewrite this as:
\[
w \geq 8 \times \frac{9}{5}
\]
Calculating that:
\[
8 \times \frac{9}{5} = \frac{72}{5} = 14.4
\]
So, \( \frac{72}{5} = 14 \frac{2}{5} \). Thus,
\[
w \geq 14 \frac{2}{5}
\]
So the correct response is:
- **w ≥ 14 2/5 (or w is greater than or equal to 14 and 2 fifths)**
### Question 3:
Since the solution involves \( w \geq 14 \frac{2}{5} \), we will use a closed circle at \( 14 \frac{2}{5} \) to denote that it includes this value (since it is "greater than or equal to"), and we shade to the right to indicate all values greater than \( 14 \frac{2}{5} \).
Thus, the correct response is:
- **Closed circle, shade right.**
To sum up the answers:
1. Divide \(\frac{5}{9}\) on both sides of the inequality.
2. w ≥ 14 2/5.
3. Closed circle, shade right.