Question

How many solutions does the following equation have?

13 - |3x-9| = 2

It has _____ solutions

Answer 1

2

Explanation:

`13-|3x-9|=2`

Subtract 13 on both sides.

`-|3x-9|=2-13`

Simplify right hand side.

`-|3x-9|=-11`

Take the opposite of both sides (also known as multiply both sides by -1).

`|3x-9|=11`.

Let u=3x-9.

Since we have |u|=positive, we will have two solutions for x.

If we had |u|=negative, we will have no solutions for x.

If we had |u|=0, we would have one solution for x.

Answer 2

`13 - |3x-9| = 2\\|3x-9|=11\\3x-9=11\vee 3x-9=-11\\3x=20 \vee 3x=-2\\x=(20)/(3) \vee x=-(2)/(3)`

TWO