How do you graph and solve #|1/x| > 2 #?

Question

1392 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-29T17:51:09

The solution is #x in(0,1/2)uu (-1/2,0)#

graph{(y-|1/x|)(y-2)=0 [-10, 10, -5, 5]}

#x!=0#

For absolute values, there are #2# solutions.

#1/x>2#

#=>#, #1/x-2>0#

#(1-2x)/x>0#

BY a sign chart the solution is #S_1= x in (0,1/2)#

and

#-1/x<2#

#=>#, #1/x+2>0#

#(1+2x)/x>0#

BY a sign chart the solution is #S_2=x in (-1/2,0)#

The solution is

#S=S_1uuS_2#