Question

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

Answer 1

`|a - 5| = 8 xx 5`

We need to consider two separate situations.

a) The absolute value is positive
b) The absolute value is negative

Starting with the positive case:

`a - 5 = 40`

`a = 45`

Now for the negative case:

`-(a - 5) = 40`

`-a + 5 = 40`

`-a = 35`

`a = -35`

Hence, the solution set is `{-35, 45}`.

Hopefully this helps!

Answer 2

`a= 45" "` or `" "a = -35`

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 `8`, the opposite of dividing by `8`.

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

Since `8/8= 1`, you have

`a -5 = 40`

`a-5` has two possible values. Solve for both values.

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

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

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

Since `-5+ 5 = 0` and `40+5 = +45`, you have

`a= + 45`

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

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

Once again, `-5 + 5 = 0` and `-40 + 5 = -35`

`a = -35`