# How do you solve #abs(a-5)/8=5#?

##### 2 Answers

We need to consider two separate situations.

a) The absolute value is positive

b) The absolute value is negative

Starting with the positive case:

Now for the negative case:

Hence, the solution set is

Hopefully this helps!

#### Explanation:

Absolute value can be negative inside or positive inside. When the value comes out of the absolute value sign it is always positive.

First, multiply both sides by

#(a- 5)/ 8 xx 8 = 5 xx 8#

Since

# a -5 = 40#

#(a-5) = + 40" "# or#" " a-5 = -40#

#a-5 = + 40 -># add#5# to both sides

#a- cancel(5) + cancel(5) = + 40 + 5#

Since

#a= + 45#

#a-5 = -40 -># add#5# to both sides

#a - cancel(5) + cancel(5) = -40 +5#

Once again,

#a = -35#