Question

in order to avoid heavy traffic, antonio can drive home after working less than 7 hours or after whours. how can this be written as a single compound inequality?\
\\(\boldsymbol{7 < h < 9}\\)\
\\(\boldsymbol{7 > h > 9}\\)\
\\(\boldsymbol{h < 7}\\) or \\(\boldsymbol{h > 9}\\)\
\\(\boldsymbol{h > 7}\\) or \\(\boldsymbol{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 (assuming the "after w hours" is a typo and should be "after 9 hours" based on the options). A compound inequality for "or" situations with these two conditions is \( h < 7 \) or \( h > 9 \). We check the options:

• \( 7 < h < 9 \) means between 7 and 9, which is not what we want.
• \( 7 > h > 9 \) is impossible as a number can't be both less than 7 and greater than 9.
• \( h > 7 \) or \( h < 9 \) would include all numbers except between 7 and 9, which is not correct.
• \( h < 7 \) or \( h > 9 \) matches the two conditions (less than 7 or more than 9).

Answer:

C. \( h < 7 \) or \( h > 9 \)