What is 4x-(17)/x-4+10x-3/2 x-3>8x-30/2 x-7 ?

The solution to 4x-(17)/x-4+10x-3/2 x-3>8x-30/2 x-7 is -sqrt(34/39) sqrt(34/39)

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4x-(17)/x-4+10x-3/2 x-3>8x-30/2 x-7

4 x - \frac{17}{x} - 4 + 10 x - \frac{3}{2} x - 3 > 8 x - \frac{30}{2} x - 7

- \frac{34}{39} < x < 0 or x > \frac{34}{39}

Interval Notation

(- \frac{34}{39}, 0) \cup (\frac{34}{39}, \infty)

Decimal Notation

- 0.93369 \dots < x < 0 or x > 0.93369 \dots

Solution steps

4 x - \frac{17}{x} - 4 + 10 x - \frac{3}{2} x - 3 > 8 x - \frac{30}{2} x - 7

Rewrite in standard form

\frac{39 x ^{2} - 34}{x} > 0

Factor

\frac{39 x ^{2} - 34}{x} : \frac{( 39 x + 34 ) ( 39 x - 34 )}{x}

\frac{( 39 x + 34 ) ( 39 x - 34 )}{x} > 0

Identify the intervals

- \frac{34}{39} < x < 0 or x > \frac{34}{39}

(3 x + 3) (5 x - 3) > 0

\frac{( x - 3 )}{( x ^{2} + 9 x - 22 )} < 0

4 x^{2} - 4 x + 3 < 0

\frac{( 2 x - 3 )}{6} - \frac{( x - 1 )}{2} > 7

\frac{x}{2} + 1 \leq \frac{x}{( 3 )} + \frac{1}{2}

What is 4x-(17)/x-4+10x-3/2 x-3>8x-30/2 x-7 ?
The solution to 4x-(17)/x-4+10x-3/2 x-3>8x-30/2 x-7 is -sqrt(34/39)<x<0\lor x>sqrt(34/39)