Question

Find y
y= |x−5| + |x+5| (if x>5)

Answer 1

`y=2x` if
`x>5`.

Explanation:

`|x-5|=x-5 \text{ if } x-5 \ge 0`. This means when
`x \ge 5`.

`|x-5|=-(x-5) \text{ if } x-5 \le 0`. This means when
`x \le 5`.

It doesn't matter where the 5 is included since either
`x-5` or
`-(x-5)` would product 0 at
`x=5`.

`|x+5|=x+5 \text{ if } x+5 \ge 0`. This means when
`x \ge -5`.

`|x+5|=-(x+5) \text{ if } x+5 \le 0`. This means when
`x \le -5`.

The same statement here about
`x=-5` as I about
`x=5` with the earlier expression.

So anyways we have
`x>5`.

This means
`y=|x-5|+|x+5|` can be rewritten as

`y=(x-5)+(x+5)=(x+x)+(-5+5)=2x+0=2x`.

`y=2x`