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?\
$h > 7$ or $h < 9$\
$h < 7$ or $h > 9$\
$7 < h < 9$\
$7 > h > 9$

Explanation:

Step1: Analyze the problem statement

Let \( h \) represent the number of hours Antonio works. The problem states he can drive home after working less than 7 hours or more than 9 hours. So we need to translate "less than 7" and "more than 9" into inequalities.

Step2: Translate "less than 7" and "more than 9"

"Less than 7" is \( h < 7 \), and "more than 9" is \( h > 9 \). The compound inequality is the "or" of these two, so \( h < 7 \) or \( h > 9 \).

Step3: Eliminate other options

• \( h > 7 \) or \( h < 9 \): This is the opposite of what's needed.
• \( 7 < h < 9 \): This represents between 7 and 9, not what's needed.
• \( 7 > h > 9 \): This is impossible as a number can't be both less than 7 and greater than 9.

Answer:

B. \( h < 7 \) or \( h > 9 \) (assuming the second option is labeled B, if the original options had labels, but based on the content, the correct one is the second box with \( h < 7 \) or \( h > 9 \))