Question

In the given problem, solve and graph.

Express answers in both inequality and interval notation.

$\frac{1}{x}<4$

Answer 1

$\frac{1}{x}<4$

$\frac{1}{x}-4<0$

$\frac{1-4x}{x}<0$

	x<0	x=0	0<x<$\frac{1}{4}$	x=$\frac{1}{4}$	x>$\frac{1}{4}$
-4x+1	+	+	+	0	-
x	-	0	+	+	+
$\frac{1-4x}{x}$	-	undefined	+	0	-

$\left[\begin{array}{cc}Solution:& x<0orx>\frac{1}{4}\\ Decimal:& x<0orx>0.25\\ IntervalNotation:& (-\infty ,0)\cup (\frac{1}{4},\infty )\end{array}\right]$