The solution to 9/x >x is x<-3\lor 0<x<3

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9/x >x

Solution

\frac{9}{x} > x

x < - 3 or 0 < x < 3

Interval Notation

(- \infty, - 3) \cup (0, 3)

Solution steps

\frac{9}{x} > x

Rewrite in standard form

\frac{9 - x ^{2}}{x} > 0

Factor

\frac{9 - x ^{2}}{x} : \frac{- ( x + 3 ) ( x - 3 )}{x}

\frac{- ( x + 3 ) ( x - 3 )}{x} > 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x + 3 ) ( x - 3 ) ) ( - 1 )}{x} < 0 \cdot (- 1)

Simplify

\frac{( x + 3 ) ( x - 3 )}{x} < 0

Identify the intervals

x < - 3 or 0 < x < 3

- (4)^{2}

y, y - ∣ x ∣ = 4

4 x^{2} - 9 x + 5

∣ 6 v + 18 ∣ = 6

(\frac{3}{5} - \frac{1}{4}) \cdot \frac{2}{3}