Question

How do you solve `5abs(q + 6)=20`?

Answer 1

`q=-2; q=-10`

Given: `5abs(q + 6) = 20`
`abs(q+6) = 4`

Absolute value is the distance a given number is from zero. This means that `q+6 = 4` or `q+6 = -4`

`q+6 =4`
`q = -2`

`q+6 = -4`
`q=-10`

I hope that was helpful.

Answer 2

Consider two possibilities:
`q<-6` and `q>-6`
(note by observation we can eliminate `q=-6`)

If `q<-6`
then `(q+6)` is negative and
`abs(q+6)` is equivalent to `-(q+6)`
and the equation becomes
`5 (-(q+6)) = 20`
`-q-6 = 4`
`q=-10`

If `q>-6`
then `(q+6)` is positive and
`abs(q+6)` is equivalent to `(q+6)`
and the equation becomes:
`5(q+6) = 20`
`q+6 = 4`
`q=-2`

The two solutions to this equation are
`q=-10` and `q=-2`