What is ((X-2)/X)^2<= 6(1-2/X)-8 ?

The solution to ((X-2)/X)^2<= 6(1-2/X)-8 is -2<= X<=-2/3

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((X-2)/X)^2<= 6(1-2/X)-8

(\frac{X - 2}{X})^{2} \leq 6 (1 - \frac{2}{X}) - 8

- 2 \leq X \leq - \frac{2}{3}

Solution steps

(\frac{X - 2}{X})^{2} \leq 6 (1 - \frac{2}{X}) - 8

Rewrite in standard form

\frac{3 X ^{2} + 8 X + 4}{X ^{2}} \leq 0

Factor

\frac{3 X ^{2} + 8 X + 4}{X ^{2}} : \frac{( 3 X + 2 ) ( X + 2 )}{X ^{2}}

\frac{( 3 X + 2 ) ( X + 2 )}{X ^{2}} \leq 0

Identify the intervals

- 2 \leq X \leq - \frac{2}{3}

- 8 b - 11 = - 9 b - 15

\frac{1}{2} + \frac{1}{2} - \frac{1}{4}

3 x^{4} + 3 x^{2} - 6

(\frac{2}{3}) 3

64 x^{3} + 8 y^{6}

What is ((X-2)/X)^2<= 6(1-2/X)-8 ?
The solution to ((X-2)/X)^2<= 6(1-2/X)-8 is -2<= X<=-2/3