How do you solve $|(x+1)/x| > 2$ , and represent the answer in interval notation?

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Answer 1 · 2018-05-20T18:02:20

The solution is $x in (-1/3,0) uu(0,1)$

This is an inequality with absolute values

$|(x+1)/x|>2$

The solutions are

${((x+1)/x>2),(-(x+1)/x>2):}$

$<=>$ , ${((x+1)/x-2>0),(-(x+1)/x-2>0):}$

$<=>$ , ${((x+1-2x)/x>0),((-x-1-2x)/x>0):}$

$<=>$ , ${((1-x)/x>0),((-3x-1)/x>0):}$

Solve the inequalities with a sign chart

$<=>$ , ${(x in (0,1)),(x in (-1/3,0)):}$

The solution is $x in (-1/3,0) uu(0,1)$

graph{|(x+1)/x|-2 [-4.93, 4.934, -2.465, 2.465]}

How do you solve |(x+1)/x| > 2|(x+1)/x| > 2, and represent the answer in interval notation?