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?
A. [tex]$7\ \textless \ h\ \textless \ 9$[/tex]
B. [tex]$7\ \textgreater \ h\ \textgreater \ 9$[/tex]
C. [tex]$h\ \textless \ 7$[/tex] or [tex]$h\ \textgreater \ 9$[/tex]
D. [tex]$h\ \textgreater \ 7$[/tex] or [tex]$h\ \textless \ 9$[/tex]
Answer (2)
Express the condition 'less than 7 hours' as an inequality: h < 7 .
Express the condition 'more than 9 hours' as an inequality: 9"> h > 9 .
Combine the two inequalities using 'or' to represent the compound inequality: h < 7 or 9"> h > 9 .
The single compound inequality is: 9}"> h < 7 or h > 9 .
Explanation
Understanding the Problem Let h represent the number of hours Antonio works. We are given that Antonio can drive home either after working less than 7 hours or after working more than 9 hours. We need to express this condition as a single compound inequality.
Expressing 'less than 7 hours' The condition 'less than 7 hours' can be written as the inequality h < 7 .
Expressing 'more than 9 hours' The condition 'more than 9 hours' can be written as the inequality 9"> h > 9 .
Combining the Inequalities Since Antonio can drive home either after working less than 7 hours or after working more than 9 hours, we combine the two inequalities using 'or'. The compound inequality is h < 7 or 9"> h > 9 .
Examples
Understanding compound inequalities is useful in many real-life situations. For example, a thermostat might be set to turn on the heat if the temperature is below 60 degrees or turn on the air conditioning if the temperature is above 80 degrees. This can be written as T < 60 or 80"> T > 80 , where T is the temperature. Similarly, in manufacturing, a machine might be programmed to stop if a measurement is less than a certain value or greater than another value, ensuring that the products meet certain specifications.
Antonio can leave work to avoid traffic if he works less than 7 hours or more than 9 hours. This can be expressed as the compound inequality: 9"> h < 7 or h > 9 . Therefore, the correct answer is option C.
;
