# How do you write an absolute value inequality to represent [-10,10]?

May 29, 2018

$y = \left\mid x \right\mid$

May 29, 2018

$\left[- 10 , 10\right] = \left\{x \in \mathbb{R} : | x | \le 10\right\}$.

#### Explanation:

We know that, $\left[a - \delta , a + \delta\right] = \left\{x \in \mathbb{R} : | x - a | \le \delta\right\}$,

where, $x , a , \delta \in \mathbb{R} \mathmr{and} \delta > 0$.

We have, $a - \delta = - 10 , a + \delta = 10 , \text{ so that, } a = 0 , \delta = 10$.

$\therefore \left[- 10 , 10\right] = \left\{x \in \mathbb{R} : | x | \le 10\right\}$.