Question

in order to avoid heavy traffic, antonio can drive home after working less than 7 hours or after working more than 9 hours. how can this be written as a single compound inequality?
○ 7 < h < 9
○ 7 > h > 9
○ h < 7 or h > 9
○ h > 7 or h < 9

Explanation:

Let \( h \) represent the number of hours Antonio works. The problem states he can drive home after working less than 7 hours (so \( h < 7 \)) or after working more than 9 hours (so \( h > 9 \)). We need to find the compound inequality that represents this "or" situation.

• Option \( 7 < h < 9 \) represents hours between 7 and 9, which is the opposite of what we need.
• Option \( 7 > h > 9 \) is not a valid inequality because a number can't be both less than 7 and greater than 9 at the same time.
• Option \( h > 7 \) or \( h < 9 \) represents hours outside the range of 7 to 9 but in the wrong direction (it includes 7 - 9 hours in a way that doesn't match the problem).
• Option \( h < 7 \) or \( h > 9 \) correctly represents the two conditions given: working less than 7 hours or more than 9 hours.

Answer:

\( h < 7 \) or \( h > 9 \) (the third option)