Question

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

Answer 1

Answer:

y=-x+5+-x-5

Step-by-step explanation:

In absolute value, make the content inside the bars the opposite of what it was before. X is less than -5, but the number it is is still unknown, meaning it should still be written as x.

Answer 2

Answer:

$y=-10$

Step-by-step explanation:

Use the definition of absolute value

$|x| = x\,\,\,\mbox{for}\,\,\,x\geq 0\\|x| = -x\,\,\,\mbox{for}\,\,\,x< 0$

Consider the first term:

$|x-5| = -(x-5) = 5-x \,\,\,\mbox{for}\,\,\,x-5\geq0\implies x\geq5\\|x-5| = x-5 \,\,\,\mbox{for}\,\,\,x-5$

Since we are given that x<-5, only the second form of this absolute value applies, namely (x-5)

Consider the second term and apply the same reasoning. You will see that only one form applies

$|x+5|=-(x+5)=-x-5\,\,\,\mbox{for}\,\,\,x$

Putting it all together:

$y=|x-5|+|x+5|=(x-5)+(-x-5)=-10\,\,\,\mbox{for}\,\,\,x$