Answer:
[tex]y=2x[/tex] if [tex]x>5[/tex].
Step-by-step explanation:
[tex]|x-5|=x-5 \text{ if } x-5 \ge 0[/tex]. This means when [tex]x \ge 5[/tex].
[tex]|x-5|=-(x-5) \text{ if } x-5 \le 0[/tex]. This means when [tex]x \le 5[/tex].
It doesn't matter where the 5 is included since either [tex]x-5[/tex] or [tex]-(x-5)[/tex] would product 0 at [tex]x=5[/tex].
[tex]|x+5|=x+5 \text{ if } x+5 \ge 0[/tex]. This means when [tex]x \ge -5[/tex].
[tex]|x+5|=-(x+5) \text{ if } x+5 \le 0[/tex]. This means when [tex]x \le -5[/tex].
The same statement here about [tex]x=-5[/tex] as I about [tex]x=5[/tex] with the earlier expression.
So anyways we have [tex]x>5[/tex].
This means [tex]y=|x-5|+|x+5|[/tex] can be rewritten as
[tex]y=(x-5)+(x+5)=(x+x)+(-5+5)=2x+0=2x[/tex].
[tex]y=2x[/tex]
