Question

Rewrite the expressions without the absolute value sign.

|x+12| , if x>−11

Answer 1

Answer:

|x+12| = -(x+12); x>-11

Step-by-step explanation:

You have the following function

$|x+12|\ if\ x>-11$   (1)

you need to write the same expression but with no absolute value sign.

You use the following equivalence for a function with absolute value:

$|x-a|=x-a\ \ \ if\ x>a\\\\|x-a|=-(x-a)\ \ \ if\ x<a\\\\|x-a|=0\ \ \ if\ x=a$

with a constant

In the case of the expression (1), you have:

$|x+12|=|x-(-12)|\\\\x>-11$

So, x > a, and the solution is:

$|x+12|=|x-(-12)|=-(x-(-12))=-(x+12)$

-(x+12)