The solution to 4/x >x is x<-2\lor 0<x<2

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4/x >x

Solution

\frac{4}{x} > x

x < - 2 or 0 < x < 2

Interval Notation

(- \infty, - 2) \cup (0, 2)

Solution steps

\frac{4}{x} > x

Rewrite in standard form

\frac{4 - x ^{2}}{x} > 0

Factor

\frac{4 - x ^{2}}{x} : \frac{- ( x + 2 ) ( x - 2 )}{x}

\frac{- ( x + 2 ) ( x - 2 )}{x} > 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x + 2 ) ( x - 2 ) ) ( - 1 )}{x} < 0 \cdot (- 1)

Simplify

\frac{( x + 2 ) ( x - 2 )}{x} < 0

Identify the intervals

x < - 2 or 0 < x < 2

2 x - 5 x = 3 x + 12

c^{2} = 121

- 42 - 6 n = - 30

\frac{9}{5} (11) + 32

12 - 5 (x + 3) = 8 x - 5