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

Explanation:

Step1: Analyze the problem statement

The problem states that Antonio can drive home after working less than 7 hours or after working more than 9 hours. Let \( h \) represent the number of hours worked.

Step2: Translate the conditions into inequalities

• "Less than 7 hours" can be written as \( h < 7 \).
• "More than 9 hours" can be written as \( h > 9 \).

Since the situation is "or" (either less than 7 or more than 9), we combine these two inequalities with the "or" operator.

Step3: Evaluate the given options

• Option 1: \( h < 7 \) or \( h > 9 \) matches our derived compound inequality.
• Option 2: \( 7 > h > 9 \) is impossible because a number cannot be both greater than 9 and less than 7 at the same time.
• Option 3: \( h > 7 \) or \( h < 9 \) represents a different range (between 7 and 9 is excluded, but our problem requires outside 7 - 9, but this option includes values like 8 which is between 7 and 9, which is incorrect).
• Option 4: \( 7 < h < 9 \) represents the range between 7 and 9, which is the opposite of what we need (we need outside this range).

Answer:

\( h < 7 \) or \( h > 9 \) (the first option among the given choices)