if you subtract from an absolute value inequality, do you switch the sign?

Question

For example:
|5+x|<20
do you keep it:
x<15
or do you switch the < to a >, so it is
x>15
If you don't switch it, and it is
x<15,
and you have to solve
5+x<-20
x<-25,
how do you graph it on a number line?

(p.s. please don't get mad at me for asking a homework q. i swear that this is an example q and is not from my actual homework.)

Answer 1

You have to break the absolute value inequality into two parts, since it could be positive OR negative. If 5+x is positive, your way is right. If 5+x is negative but greater then -20 it still works.

5 + x > -20
x > -25

To graph on a number line, place an open dot over -25 and another open dot over 15, then connect the dots with a darkened segment. If it had been less than or equal to, you'd fill in the dots.
So x is between -25 and 15, or -25 < x < 15

Answer 2

that type of equation has two answers. first you drop the absolute value signs and than get: 5+x<20 and 5+x>-20. this becomes -20<5+x<20
which becomes -25

Answer 3

switch it.
-25 -20 ,..........-5
<____________no colored in circle

hope i helped you