Question

How do you solve `abs(-2r-1)=11`?

Answer 1

`r = -6, r = 5`

Explanation:

This is an absolute value equation meaning that we need to split this into two equations; the original equation and the opposite of it:

`-2r-1 = 11` and `-2r-1=-11`
Notice that the `11` became `-11`.

Now we can solve this by simplifying. Let's simplify the first one:
`-2r-1 = 11`
`-2r = 12`
`r = -6`

Second one:
`-2r-1 = -11`
`-2r = -10`
`r = 5`

Now let's check our work by plugging what we got for r back into the original equation `|-2r-1| = 11`.
`|-2(-6) -1|= 11`
`|12-1| = 11`
`11 = 11` :)

`|-2(5)-1|=11`
`|-10-1| = 11`
`|-11| = 11`
`11 = 11` :)

So our two solutions are `r = -6` and `r = 5`.