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

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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

$S=S_1uuS_2$

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