Respuesta :
Answer:
[tex]y=2x[/tex] if [tex]x>5[/tex]
Problem:
"Rewrite without absolute value for the given conditions: y=|x−5|+|x+5|, if x>5"
Step-by-step explanation:
Let's figure out when the insides of the absolute values are positive and negative, and then see where the given condition that x>5 fits into that.
[tex]|x-5|=x-5[/tex] if [tex]x-5[/tex] is positive or 0,[tex]\ge 0[/tex].
[tex]x-5 \ge 0[/tex]
Add 5 on both sides:
[tex]x \ge 5[/tex].
[tex]|x-5|=-(x-5)[/tex] if [tex]x-5[/tex] is negative or zero, [tex]\le 0[/tex].
[tex]x-5 \le 0[/tex]
Add 5 on both sides:
[tex]x \le 5[/tex]
Since [tex]x>5[/tex] then we will choose [tex]|x-5|=x-5[/tex].
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[tex]|x+5|=x+5[/tex] if [tex]x+5[/tex] is positive or 0,[tex]\ge 0[/tex].
[tex]x+5 \ge 0[/tex]
Subtract 5 on both sides:
[tex]x \ge -5[/tex].
[tex]|x+5|=-(x+5)[/tex] if [tex]x+5[/tex] is negative or zero, [tex]\le 0[/tex].
[tex]x+5 \le 0[/tex]
Subtract 5 on both sides:
[tex]x \le -5[/tex]
Since [tex]x>5[/tex] then we will choose [tex]|x+5|=x+5[/tex].
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[tex]y=|x−5|+|x+5|[/tex] with [tex]x>5[/tex]:
[tex]y=(x-5)+(x+5)[/tex]
[tex]y=(x+x)+(-5+5)[/tex]
[tex]y=(2x)+(0)[/tex]
[tex]y=2x+0[/tex]
[tex]y=2x[/tex]
