What is 1/(x-2)+2/(3x-21)>= 0 ?

The solution to 1/(x-2)+2/(3x-21)>= 0 is 2 7

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1/(x-2)+2/(3x-21)>= 0

\frac{1}{x - 2} + \frac{2}{3 x - 21} \geq 0

2 < x \leq 5 or x > 7

Interval Notation

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

Solution steps

\frac{1}{x - 2} + \frac{2}{3 x - 21} \geq 0

Rewrite in standard form

\frac{5 x - 25}{( x - 2 ) ( x - 7 )} \geq 0

Factor

\frac{5 x - 25}{( x - 2 ) ( x - 7 )} : \frac{5 ( x - 5 )}{( x - 2 ) ( x - 7 )}

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

Divide both sides by

5

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

Simplify

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

Identify the intervals

2 < x \leq 5 or x > 7

x^{2} - 10 x = - 21

2 x - \frac{1}{3} \leq 8

\frac{( \frac{4}{9} ) ^{- 2}}{( \frac{27}{8} ) ^{- 3}}

lo g_{\frac{1}{4}} (5)

\frac{75}{48}

What is 1/(x-2)+2/(3x-21)>= 0 ?
The solution to 1/(x-2)+2/(3x-21)>= 0 is 2<x<= 5\lor x>7