Select all numbers that are solutions to the inequality [tex]c\ \textless \ 7[/tex].
7.01
7
0.07
6.99
6
8
Answer (2)
The problem requires identifying numbers less than 7.
Check each number against the inequality c < 7 .
7.01, 7, and 8 are not less than 7.
0.07, 6.99, and 6 are less than 7, so the final answer is 0.07 , 6.99 , 6 .
Explanation
Understanding the Inequality We are given the inequality c < 7 , which means we are looking for numbers that are strictly less than 7. We need to check each of the given numbers to see if they satisfy this condition.
Checking Each Number Let's examine each number:
7.01: Is 7.01 less than 7? No, it is greater. So, 7.01 is not a solution.
7: Is 7 less than 7? No, 7 is equal to 7. So, 7 is not a solution.
0.07: Is 0.07 less than 7? Yes, it is. So, 0.07 is a solution.
6.99: Is 6.99 less than 7? Yes, it is. So, 6.99 is a solution.
6: Is 6 less than 7? Yes, it is. So, 6 is a solution.
8: Is 8 less than 7? No, it is greater. So, 8 is not a solution.
Identifying the Solutions Therefore, the numbers that are solutions to the inequality c < 7 are 0.07, 6.99, and 6.
Examples
Imagine you're setting a maximum height for a doorway. The inequality c < 7 represents that the height of anyone passing through the doorway must be less than 7 feet to avoid bumping their head. Checking each person's height against this inequality ensures only those shorter than 7 feet can pass through comfortably. This concept applies to various scenarios, such as weight limits on bridges, speed limits on roads, or age restrictions for certain activities, where adhering to an upper bound is crucial.
The solutions to the inequality c < 7 are the numbers that are strictly less than 7. The numbers that satisfy this condition from the given list are 0.07, 6.99, and 6.
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