In order to qualify for a role in a play, an actor must be taller than 64 inches but shorter than 68 inches. The inequality [tex]$64\ \textless \ x\ \textless \ 68$[/tex], where [tex]$x$[/tex] represents height, can be used to represent the height range. Which is another way of writing the inequality?
A. [tex]$x\ \textgreater \ 64$[/tex] and [tex]$x\ \textless \ 68$[/tex]
B. [tex]$x\ \textgreater \ 64$[/tex] or [tex]$x\ \textless \ 68$[/tex]
C. [tex]$x\ \textless \ 64$[/tex] and [tex]$x\ \textless \ 68$[/tex]
D. [tex]$x\ \textless \ 64$[/tex] or [tex]$x\ \textless \ 68$[/tex]
Answer (1)
The inequality 64 < x < 68 means x is greater than 64 and less than 68.
This can be written as 64"> x > 64 and x < 68 .
Comparing with the options, 64"> x > 64 and x < 68 is the correct representation.
Therefore, the answer is 64"> x > 64 and x < 68 .
Explanation
Understanding the Inequality We are given the inequality 64 < x < 68 , which represents the height range for an actor to qualify for a role in a play. We need to find an equivalent way to express this inequality from the given options.
Expressing the Inequality The inequality 64 < x < 68 means that x is greater than 64 and x is less than 68. In mathematical terms, this can be written as 64"> x > 64 and x < 68 .
Comparing with the Options Now, let's compare this with the given options:
64"> x > 64 and x < 68
64"> x > 64 or x < 68
x < 64 and x < 68
x < 64 or x < 68
The first option, 64"> x > 64 and x < 68 , matches our interpretation of the inequality 64 < x < 68 .
Final Answer Therefore, the correct way to write the inequality 64 < x < 68 is 64"> x > 64 and x < 68 .
Examples
Imagine you're setting up a basketball game and need players within a specific age range for fair competition. If the rules state that players must be older than 10 years but younger than 14 years, you can express this age requirement as 10 < x < 14 , where x is the player's age. This is the same as saying a player must be older than 10 AND younger than 14 to participate. Understanding how to express these constraints helps ensure fair and balanced gameplay.
