Question

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

Answer 1

`{-9.4,7}`

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.
`5x+6=41`
and
`5x+6=-41`
so the distance from zero means from both the positive and negative directions

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

`5x+6=-41`
`5x=-47`
`x=-47/5=-9.4`

`{-9.4,7}`