Question

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

Answer 1

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

Here's how I did it:

Explanation:

`(|r+5|)/2=3`

First, multiply both sides by `2`:
`(|r+5|)/cancel(2) cancel(color(red)(*2)) = 3 color(red)(*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 quadcolor(red)(-quad5) = 6 quadcolor(red)(-quad5)`
`r = 1`

Now let's look at `r + 5 = -6`
Subtract `5` from both sides of the equation:
`r + 5 quadcolor(red)(-quad5) = -6 quadcolor(red)(-quad5)`
`r = -11`

Now that we found the values of `r`, let's check them by plugging them back into the original equation:
`(|r+5|)/2=3`

`|1 + 5| = 6`

`|6| = 6`

`6 = 6`

Yes, `r = 1`!

Now let's check `r=-11`:
`(|-11+5|)/2=3`

`|-6|=6`

`6=6`

Yes, `r=-11`!

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

Hope this helps!