# How do you solve abs(11-4x)=7?

Sep 22, 2016

$x = 1 \text{ and } x = \frac{9}{2}$

#### Explanation:

This is the same as $| \pm 7 | = + 7$

So $11 - 4 x = \pm 7$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Consider the case "11-4x=-7"

$4 x = 18 \implies x = \frac{18}{4} \to \textcolor{b l u e}{x = \frac{9}{2}}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Consider the case "11-4x=+7"

$4 x = 4 \implies x = \frac{4}{4} \to \textcolor{b l u e}{x = 1}$