Question

Rewrite without absolute value for the given conditions: y=|x−5|+|x+5|, if x>5

Answer 1

Answer:

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

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.

$|x-5|=x-5$ if $x-5$ is positive or 0,$\ge 0$.

$x-5 \ge 0$

Add 5 on both sides:

$x \ge 5$.

$|x-5|=-(x-5)$ if $x-5$ is negative or zero, $\le 0$.

$x-5 \le 0$

Add 5 on both sides:

$x \le 5$

Since $x>5$ then we will choose $|x-5|=x-5$.

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$|x+5|=x+5$ if $x+5$ is positive or 0,$\ge 0$.

$x+5 \ge 0$

Subtract 5 on both sides:

$x \ge -5$.

$|x+5|=-(x+5)$ if $x+5$ is negative or zero, $\le 0$.

$x+5 \le 0$

Subtract 5 on both sides:

$x \le -5$

Since $x>5$ then we will choose $|x+5|=x+5$.

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$y=|x−5|+|x+5|$ with $x>5$:

$y=(x-5)+(x+5)$

$y=(x+x)+(-5+5)$

$y=(2x)+(0)$

$y=2x+0$

$y=2x$