Question

How do you solve `9| 3+ x | = 36`?

Answer 1

`x=1,-7`

Explanation:

To start, we need to see that the `3+x` term is sitting inside an absolute value sign, so we need to isolate that. We can do that by dividing by 9 on both sides:

`9|3+x|=36`

`|3+x|=4`

The absolute value sign means that whatever the value of `3+x` is on the inside, it will always be positive on the outside. For example:

`|4|=4`, `|-4|=4`

So the value of `3+x` could be positive or it could be negative. So we need to look at both cases. Let's do the positive first:

`3+x=4`

`x=1`

Now the negative:

`-(3+x)=4`

`-3-x=4`

`-x=7`

`x=-7`