How do you graph and solve #|x – 1| ≥ 2 #?

1 Answer
Nov 25, 2015

Answer:

One way is to consider the two cases for the absolute value separately.
Since this is a relationship in one variable it can be graphed on a number line as:
enter image source here

Explanation:

Case 1: #color(black)((x-1)>=0)#
#color(white)("XXX")abs(x-1)>=2#

#color(white)("XXX")x-1 >=2#

#color(white)("XXX")x >= 3#

Case 2: #color(black)(x-1) < 0#
#color(white)("XXX")abs(x-1) >= 2#

#color(white)("XXX")1-x >=2#

#color(white)("XXX")-1 >= x#