Question

In the given problem, solve and graph.

Express answers in both inequality and interval notaion.

$\left|\frac{x+1}{x}\right|>2$

Answer 1

$\left|\frac{x+1}{x}\right|>2$

$\frac{x+1}{x}<-2or\frac{x+1}{x}>2$

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$\frac{x+1}{x}<-2$

$\frac{x+1}{x}+2<0$

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$\frac{x+1}{x}+2$

$=\frac{x+1}{x}+\frac{2x}{x}$

$=\frac{x+1+2x}{x}$

$=\frac{3x+1}{x}$

$\frac{3x+1}{x}<0$

$-\frac{1}{3}<x<0$

$-\frac{1}{3}<x<0or0<x<1$

$\left|\frac{x+1}{x}\right|>2:\left[\begin{array}{cc}Solution:& -\frac{1}{3}<x<0or0<x<1\\ Decimal:& -0.33333\cdots <x<0or0<x<1\\ IntervalNotation:& (-\frac{1}{3},0)\cup (0,1)\end{array}\right]$