Question
Use the inequality to answer the question.
12x−14<198
Which situation matches the inequality?
Responses
Jason makes 12 dollars per hour and gets his pay reduced by $14, making his paycheck at least $198.
Jason makes 12 dollars per hour and gets his pay reduced by $14, making his paycheck less than $198.
Jason makes 12 dollars per hour and gets a bonus of $14, making his paycheck at least
$198.
Jason makes 12 dollars per hour and gets a bonus of $14, making his paycheck less than
Answers
GPT-4o mini
To solve the inequality \( 12x - 14 < 198 \), first, we can isolate \( x \):
1. Add \( 14 \) to both sides:
\[
12x < 198 + 14
\]
\[
12x < 212
\]
2. Divide both sides by \( 12 \):
\[
x < \frac{212}{12}
\]
\[
x < 17.67
\]
This means that Jason can work less than approximately 17.67 hours.
Now, let's analyze the given situations:
1. **Jason makes 12 dollars per hour and gets his pay reduced by $14, making his paycheck at least $198.**
- This suggests that after reduction, he still ends up with at least $198, which does not match our inequality as it implies a minimum paycheck.
2. **Jason makes 12 dollars per hour and gets his pay reduced by $14, making his paycheck less than $198.**
- This matches the concept of the inequality since reducing his pay by $14 could lead to a paycheck less than $198 depending on the hours worked.
3. **Jason makes 12 dollars per hour and gets a bonus of $14, making his paycheck at least $198.**
- This again suggests his paycheck reaches at least $198, which does not match the inequality.
4. **Jason makes 12 dollars per hour and gets a bonus of $14, making his paycheck less than $198.**
- This suggests that even with a bonus, his total earnings are still under $198, which does not match the inequality.
Based on the analysis, the situation that corresponds to the inequality \( 12x - 14 < 198 \) is:
**Jason makes 12 dollars per hour and gets his pay reduced by $14, making his paycheck less than $198.**
1. Add \( 14 \) to both sides:
\[
12x < 198 + 14
\]
\[
12x < 212
\]
2. Divide both sides by \( 12 \):
\[
x < \frac{212}{12}
\]
\[
x < 17.67
\]
This means that Jason can work less than approximately 17.67 hours.
Now, let's analyze the given situations:
1. **Jason makes 12 dollars per hour and gets his pay reduced by $14, making his paycheck at least $198.**
- This suggests that after reduction, he still ends up with at least $198, which does not match our inequality as it implies a minimum paycheck.
2. **Jason makes 12 dollars per hour and gets his pay reduced by $14, making his paycheck less than $198.**
- This matches the concept of the inequality since reducing his pay by $14 could lead to a paycheck less than $198 depending on the hours worked.
3. **Jason makes 12 dollars per hour and gets a bonus of $14, making his paycheck at least $198.**
- This again suggests his paycheck reaches at least $198, which does not match the inequality.
4. **Jason makes 12 dollars per hour and gets a bonus of $14, making his paycheck less than $198.**
- This suggests that even with a bonus, his total earnings are still under $198, which does not match the inequality.
Based on the analysis, the situation that corresponds to the inequality \( 12x - 14 < 198 \) is:
**Jason makes 12 dollars per hour and gets his pay reduced by $14, making his paycheck less than $198.**