Question

Simplify without the absolute value |x+3| ; if x>2

Answer 1

`x+3` if
`x>2`

Explanation:

Recall some following basic ideas about absolute value:

`|0|=0` or I guess
`-(0)=0`

`|3|=3`

`|-3|=-(-3)` or just
`3` but there is a reason why I wrote it the way I did.

You see that the absolute value returned the same value if the value was positive.

You see that the absolute value returned the opposite value if the value was negative.

You can include 0 in either.

Let's look at
`|x+3|` alone for a second.

*
`|x+3|=x+3` if
`x+3` is positive or zero.

When is
`x+3` positive or zero? [greater than or equal to 0]

`x+3\ge 0`

Subtract 3 on both sides

`x\ge -3`

*
`|x+3|=-(x+3)` if
`x+3` is negative or zero.

When is
`x+3` negative or zero? [less or equal to 0]

`x+3\le 0`

Subtract 3 on both sides

`x\le -3`

So looking at the bullet points (the *),
`x>2` fits into the first inequality.

Therefore,
`|x+3|=x+3`.