# How do you solve abs(5x+6)=41?

Nov 3, 2016

$\left\{- 9.4 , 7\right\}$

#### Explanation:

Imagine a number line. The definition of abs value is the distance from zero, so when dealing with abs value equations you have to set up 2 different equations.
$5 x + 6 = 41$
and
$5 x + 6 = - 41$
so the distance from zero means from both the positive and negative directions

$5 x + 6 = 41$
$5 x = 35$
$x = 7$

$5 x + 6 = - 41$
$5 x = - 47$
$x = - \frac{47}{5} = - 9.4$

$\left\{- 9.4 , 7\right\}$