# How do you solve \frac { | r + 5| } { 2} = 3?

Apr 13, 2018

The solutions for $r$ are $- 11 , 1$.

Here's how I did it:

#### Explanation:

$\frac{| r + 5 |}{2} = 3$

First, multiply both sides by $2$:
$\frac{| r + 5 |}{\cancel{2}} \cancel{\textcolor{red}{\cdot 2}} = 3 \textcolor{red}{\cdot 2}$

$| r + 5 | = 6$

Since we have the absolute value by itself, we set the quantity inside the absolute value equal to the positive and negative quantity on the other side of the equation:
$r + 5 = 6$ and $r + 5 = - 6$

Let's look at $r + 5 = 6$
Subtract $5$ from both sides of the equation:
$r + 5 \quad \textcolor{red}{- \quad 5} = 6 \quad \textcolor{red}{- \quad 5}$
$r = 1$

Now let's look at $r + 5 = - 6$
Subtract $5$ from both sides of the equation:
$r + 5 \quad \textcolor{red}{- \quad 5} = - 6 \quad \textcolor{red}{- \quad 5}$
$r = - 11$

Now that we found the values of $r$, let's check them by plugging them back into the original equation:
$\frac{| r + 5 |}{2} = 3$

$| 1 + 5 | = 6$

$| 6 | = 6$

$6 = 6$

Yes, $r = 1$!

Now let's check $r = - 11$:
$\frac{| - 11 + 5 |}{2} = 3$

$| - 6 | = 6$

$6 = 6$

Yes, $r = - 11$!

So the solutions for $r$ are $- 11 , 1$.

Hope this helps!