What is 3x-1/x <= 2 ?

The solution to 3x-1/x <= 2 is x<=-1/3 \lor 0<x<= 1

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3x-1/x <= 2

3 x - \frac{1}{x} \leq 2

x \leq - \frac{1}{3} or 0 < x \leq 1

Interval Notation

(- \infty, - \frac{1}{3}] \cup (0, 1]

Decimal Notation

x \leq - 0.33333 \dots or 0 < x \leq 1

Solution steps

3 x - \frac{1}{x} \leq 2

Rewrite in standard form

\frac{3 x ^{2} - 1 - 2 x}{x} \leq 0

Factor

\frac{3 x ^{2} - 1 - 2 x}{x} : \frac{( 3 x + 1 ) ( x - 1 )}{x}

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

Identify the intervals

x \leq - \frac{1}{3} or 0 < x \leq 1

\frac{13 !}{3 ! ( 13 - 3 ) !}

x^{2} + 8 x = 0

\frac{6 x - 3}{x - 1} \geq x

2 x^{2} - 5 x + 3 \geq 0

4 - k^{2}