What is 1/(x-2)+1/(4x-28)>= 0 ?

The solution to 1/(x-2)+1/(4x-28)>= 0 is 2 7

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1/(x-2)+1/(4x-28)>= 0

\frac{1}{x - 2} + \frac{1}{4 x - 28} \geq 0

2 < x \leq 6 or x > 7

Solution steps

\frac{1}{x - 2} + \frac{1}{4 x - 28} \geq 0

Rewrite in standard form

\frac{5 x - 30}{( x - 2 ) ( x - 7 )} \geq 0

Factor

\frac{5 x - 30}{( x - 2 ) ( x - 7 )} : \frac{5 ( x - 6 )}{( x - 2 ) ( x - 7 )}

\frac{5 ( x - 6 )}{( x - 2 ) ( x - 7 )} \geq 0

Divide both sides by

5

\frac{\frac{5 ( x - 6 )}{( x - 2 ) ( x - 7 )}}{5} \geq \frac{0}{5}

Simplify

\frac{x - 6}{( x - 2 ) ( x - 7 )} \geq 0

Identify the intervals

2 < x \leq 6 or x > 7

- \frac{\frac{5}{2}}{( - \frac{15}{17} )}

\frac{15 x ^{10} y ^{9}}{5 x ^{6} y ^{2}}

x - 1 < 0

3 5^{2} + 1 2^{2} = x^{2}

\frac{10}{3 + 2 x} \leq 5

What is 1/(x-2)+1/(4x-28)>= 0 ?
The solution to 1/(x-2)+1/(4x-28)>= 0 is 2<x<= 6\lor x>7