How do you graph and solve # |2x-5| >= -1#?

1 Answer
Mar 20, 2016

Answer:

Just find when #2x-5# is negative and put a negative sign to "make" it positive for the absolute part. Answer is:

#|2x-5|> -1# for every #x inRR#

They are never equal.

Explanation:

Quick solution

The left part of the equation is an absolute, so it is always positive with a minimum of 0. Therefore, the left part is always:

#|2x-5|>=0> -1#

#|2x-5|> -1# for every #x inRR#

Graph solution

#|2x-5|#

This is negative when:

#2x-5<0#

#2x<5#

#x<5/2#

And positive when:

#2x-5>0#

#2x>5#

#x>5/2#

Therefore, for you must graph:

#-(2x-5)=-2x+5# for #x<5/2#

#2x-5# for #x>5/2#

These are both lines. Graph is:

graph{|2x-5| [-0.426, 5.049, -1.618, 1.12]}

As we can clearly see, the graph never passes through #-1# so the equal part is never true. However, it is always greater than #-1# so the answer is:

For every #x inRR# (which means #x in(-oo,+oo)#