How do you solve #abs(x-3)>=1#?

1 Answer
Apr 3, 2018

Answer:

#2 geq x geq 4#

Explanation:

From #|x-3| geq 1# it follows that #x-3 leq -1# and #x-3 geq 1#

Adding 3 to both sides of the equations we get
#x leq 2# and #x geq 4# which are our two solutions.

Also, looking at the graph of #y=|x-3|# we can see which values of y are greater than or equal to #1# and these are indeed the values where x is less than or equal to 2, and where x is greater than or equal to 4.

graph{|x-3| [-10, 10, -5, 5]}