# Question #ecdc2

Oct 3, 2016

$\left\mid x - 7850 \right\mid \le 7850$

#### Explanation:

$0 \le x \le 15700$

$0$ and $15700$ are the endpoints of an interval. Find the middle of the interval by subtracting 0 from 15700 and dividing the result by 2.

$\frac{15700 - 0}{2} = 7850$

Then write the inequality in terms of $- 7850$ and $7850$.

$\textcolor{w h i t e}{a a} 0 \textcolor{w h i t e}{a a a a a} \le x \le \textcolor{w h i t e}{a a} 15700$
$- 7850 \textcolor{w h i t e}{a a} - 7850 \textcolor{w h i t e}{a} - 7850$

$- 7850 \le x - 7850 \le 7850$
or
$x - 7850 \ge - 7850 , \textcolor{w h i t e}{a a a a a} x - 7850 \le 7850$

Written as an absolute value, this inequality becomes

$\left\mid x - 7850 \right\mid \le 7850$