Question

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 $64 < x < 68$, where $x$ represents height, can be used to represent the height range. which is another way of writing the inequality?
$x < 64$ or $x < 68$
$x > 64$ or $x < 68$
$x > 64$ and $x < 68$
$x < 64$ and $x < 68$

Explanation:

Step1: Interpret compound inequality

The inequality $64 < x < 68$ is a combined statement meaning $x$ must satisfy both $64 < x$ and $x < 68$ at the same time.

Step2: Match to option

Rewrite $64 < x$ as $x > 64$. The combined condition is $x > 64$ and $x < 68$, which matches one of the options.

Answer:

$x > 64$ and $x < 68$