What is (4x-20)/((x-2)(x-7))<0 ?

The solution to (4x-20)/((x-2)(x-7))<0 is x<2\lor 5<x<7

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(4x-20)/((x-2)(x-7))<0

\frac{4 x - 20}{( x - 2 ) ( x - 7 )} < 0

x < 2 or 5 < x < 7

Interval Notation

(- \infty, 2) \cup (5, 7)

Solution steps

\frac{4 x - 20}{( x - 2 ) ( x - 7 )} < 0

Factor

\frac{4 x - 20}{( x - 2 ) ( x - 7 )} : \frac{4 ( x - 5 )}{( x - 2 ) ( x - 7 )}

\frac{4 ( x - 5 )}{( x - 2 ) ( x - 7 )} < 0

Divide both sides by

4

\frac{\frac{4 ( x - 5 )}{( x - 2 ) ( x - 7 )}}{4} < \frac{0}{4}

Simplify

\frac{x - 5}{( x - 2 ) ( x - 7 )} < 0

Identify the intervals

x < 2 or 5 < x < 7

m^{2} + 8 m = - 3

9 x^{2} + 10 x + 1 = 0

3 + \frac{2 + 7 x}{9} = 9

4 a^{2} - 8 a - 5

\frac{18 x ^{2} y}{2 y ^{3}}

What is (4x-20)/((x-2)(x-7))<0 ?
The solution to (4x-20)/((x-2)(x-7))<0 is x<2\lor 5<x<7