# How do you write each specification as an absolute value inequality: 6.3 (is less than or equal to) h (is less than or equal to) 10.3?

Feb 10, 2017

$\left\mid h - 8.3 \right\mid \le 2$

#### Explanation:

Given $6.3 \le h \le 10.3$

The midpoint between $6.3$ and $10.3$ is $8.3$

Remember that we can subtract the same amount for both sides of an inequality and still maintain the validity of the inequality:

$\textcolor{w h i t e}{\text{XXX}} 6.3 - 8.3 \le h - 8.3 \le 10.3 - 8.3$

$\textcolor{w h i t e}{\text{XXX}} - 2 \le h - 8.3 \le 2$

which we could split up as
$\textcolor{w h i t e}{\text{XXX")-2 <= h-8.3 color(white)("X")rarrcolor(white)("X}} - \left(h - 8.3\right) \le 2$
and
$\textcolor{w h i t e}{\text{XXX}} h - 8.3 \le 2$

which recombines as
$\textcolor{w h i t e}{\text{XXX}} \left\mid h - 8.3 \right\mid \le 2$