Question

Find y y= |x−5| + |x+5| (if x>5)

Answer 1

Answer:

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

Step-by-step 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

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

$y=2x$