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

1 Answer
Shantelle
Apr 13, 2018

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!

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