Question
Sylvia worked out for more than 35 minutes total. She spent 12 minutes running, and x minutes each on 4 stations. How much time could she have spent on each station?
Write an inequality to represent the situation. Use x to represent the minutes spent on each of the stations.
12+4x>35
Excellent!
You just wrote an inequality to represent the situation. Now solve the associated equation, 12 + 4x = 35, to find the boundary for the inequality. Show your work or solve on paper.
12 + 4x > 35
12+4x
=
35
x
=
Write an inequality to represent the situation. Use x to represent the minutes spent on each of the stations.
12+4x>35
Excellent!
You just wrote an inequality to represent the situation. Now solve the associated equation, 12 + 4x = 35, to find the boundary for the inequality. Show your work or solve on paper.
12 + 4x > 35
12+4x
=
35
x
=
Answers
GPT-4o mini
To solve the equation \(12 + 4x = 35\), we need to isolate \(x\). Here are the steps:
1. **Start with the equation**:
\[
12 + 4x = 35
\]
2. **Subtract 12 from both sides**:
\[
4x = 35 - 12
\]
\[
4x = 23
\]
3. **Divide both sides by 4** to solve for \(x\):
\[
x = \frac{23}{4}
\]
\[
x = 5.75
\]
Now that we have solved the equation, \(x = 5.75\). This means that each station took 5.75 minutes when the total workout time is exactly 35 minutes.
### Summary:
- The boundary for the inequality \(12 + 4x > 35\) is \(x = 5.75\).
- Therefore, for Sylvia to meet her goal of more than 35 minutes, the time spent on each station must be greater than 5.75 minutes, i.e., \(x > 5.75\).
1. **Start with the equation**:
\[
12 + 4x = 35
\]
2. **Subtract 12 from both sides**:
\[
4x = 35 - 12
\]
\[
4x = 23
\]
3. **Divide both sides by 4** to solve for \(x\):
\[
x = \frac{23}{4}
\]
\[
x = 5.75
\]
Now that we have solved the equation, \(x = 5.75\). This means that each station took 5.75 minutes when the total workout time is exactly 35 minutes.
### Summary:
- The boundary for the inequality \(12 + 4x > 35\) is \(x = 5.75\).
- Therefore, for Sylvia to meet her goal of more than 35 minutes, the time spent on each station must be greater than 5.75 minutes, i.e., \(x > 5.75\).