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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

1 answer

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.