Question

In the given problem, solve and graph. Express answers in both inequality and interval notation. $\frac{5}{x}>3$

Answer 1

$\frac{5}{x}>3$

$\frac{5}{x}-3>0$

$\frac{5-3x}{x}>0$

	x<0	x=0	0<x<$\frac{5}{3}$	x=$\frac{5}{3}$	x>$\frac{5}{3}$
-3x+5	+	+	+	0	-
x	-	0	+	+	+
$\frac{5-3x}{x}$	-	undefined	+	0	-

$\left[\begin{array}{cc}Solution:& 0<x<\frac{5}{3}\\ Decimal:& 0<x<1.66667\dots \\ IntervalNotation:& (0,\frac{5}{3})\end{array}\right]$