How do you solve #abs(x-1)>2#?

1 Answer
Oct 31, 2016

Answer:

#x>3# or #x<-1#

Explanation:

#abs(x-1)>2#

This absolute value inequality can be rewritten as two inequalities.

#x-1>2color(white)(aaa)# or#color(white)(aa)x-1 < -2#

Add #1# to both sides.

#x-1>2color(white)(aaaaaaa)x-1<-2#
#color(white)a+1color(white)(a)+1color(white)(aa^2aaaaa)+1color(white)(aa^2)+1#

#x>3color(white)(aaaaaa)orcolor(white)(aaaaa)x<-1#