What is 2/(x-4)>= (-6)/(5-x) ?

The solution to 2/(x-4)>= (-6)/(5-x) is x<= 7/2 \lor 4<x<5

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2/(x-4)>= (-6)/(5-x)

\frac{2}{x - 4} \geq \frac{- 6}{5 - x}

x \leq \frac{7}{2} or 4 < x < 5

Solution steps

\frac{2}{x - 4} \geq \frac{- 6}{5 - x}

Rewrite in standard form

\frac{4 x - 14}{( x - 4 ) ( - x + 5 )} \geq 0

Factor

\frac{4 x - 14}{( x - 4 ) ( - x + 5 )} : \frac{2 ( 2 x - 7 )}{( x - 4 ) ( - x + 5 )}

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

Divide both sides by

2

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

Simplify

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

Identify the intervals

x \leq \frac{7}{2} or 4 < x < 5

\frac{3 - 4 i}{4 + 3 i}

(1 - \frac{1}{4})^{2}

- 7 ∣ 8 - x ∣ < - 21

k^{2} + 24 k + 23

∣ x - 3 ∣ > 6

What is 2/(x-4)>= (-6)/(5-x) ?
The solution to 2/(x-4)>= (-6)/(5-x) is x<= 7/2 \lor 4<x<5