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

Oct 30, 2017

$r = - 6 , r = 5$

#### 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:

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

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

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

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

$| - 2 \left(5\right) - 1 | = 11$
$| - 10 - 1 | = 11$
$| - 11 | = 11$
$11 = 11$ :)

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