What is 6x-5-6/x <= 0 ?

The solution to 6x-5-6/x <= 0 is x<=-2/3 \lor 0<x<= 3/2

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6x-5-6/x <= 0

6 x - 5 - \frac{6}{x} \leq 0

x \leq - \frac{2}{3} or 0 < x \leq \frac{3}{2}

Interval Notation

(- \infty, - \frac{2}{3}] \cup (0, \frac{3}{2}]

Decimal Notation

x \leq - 0.66666 \dots or 0 < x \leq 1.5

Solution steps

6 x - 5 - \frac{6}{x} \leq 0

Rewrite in standard form

\frac{6 x ^{2} - 5 x - 6}{x} \leq 0

Factor

\frac{6 x ^{2} - 5 x - 6}{x} : \frac{( 3 x + 2 ) ( 2 x - 3 )}{x}

\frac{( 3 x + 2 ) ( 2 x - 3 )}{x} \leq 0

Identify the intervals

x \leq - \frac{2}{3} or 0 < x \leq \frac{3}{2}

3 x - 2 \leq - 3 x + 6

14 x + 7 x = 21 x

∣ x ∣ > 6

3 6 - \frac{3}{2} x + 6 = 15

(3 z^{2})^{2}