# A company is making an action figure that must be at least 19.21 centimeters tall and at most 31.23 centimeters tall. How do you write a compound inequality that describes how tall the action figure can be and put the answer in set builder notation?

Sep 17, 2017

$H = \left\{x : 19.21 \le x \le 31.23 , x \in \mathbb{R}\right\}$

or

$H = \left\{x | 19.21 \le x \le 31.23 , x \in \mathbb{R}\right\}$

#### Explanation:

The figure can have a length anywhere from $19.21 \mathmr{and} 31.23$cm.

These are the upper and lower limits:

$19.21 \le x \le 31.23$

Set builder notation states that this condition must apply to all the possible values of $x$ which has to be a real number.

$H = \left\{x : 19.21 \le x \le 31.23 , x \in \mathbb{R}\right\}$