What is 4/(x-5)<= 2/(x-3) ?

The solution to 4/(x-5)<= 2/(x-3) is x<= 1\lor 3<x<5

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4/(x-5)<= 2/(x-3)

\frac{4}{x - 5} \leq \frac{2}{x - 3}

x \leq 1 or 3 < x < 5

Interval Notation

(- \infty, 1] \cup (3, 5)

Solution steps

\frac{4}{x - 5} \leq \frac{2}{x - 3}

Rewrite in standard form

\frac{2 x - 2}{( x - 5 ) ( x - 3 )} \leq 0

Factor

\frac{2 x - 2}{( x - 5 ) ( x - 3 )} : \frac{2 ( x - 1 )}{( x - 5 ) ( x - 3 )}

\frac{2 ( x - 1 )}{( x - 5 ) ( x - 3 )} \leq 0

Divide both sides by

2

\frac{\frac{2 ( x - 1 )}{( x - 5 ) ( x - 3 )}}{2} \leq \frac{0}{2}

Simplify

\frac{x - 1}{( x - 5 ) ( x - 3 )} \leq 0

Identify the intervals

x \leq 1 or 3 < x < 5

x^{2} - 10 x = 2 x - 35

- 6 x + 2 = - 5 x + 5

(2 a - 3 b) \cdot 4 b - 3 a (a - 2 b)

∣ x - 20 ∣ > 5

3 x^{2} + 15 x - 5 = 0

What is 4/(x-5)<= 2/(x-3) ?
The solution to 4/(x-5)<= 2/(x-3) is x<= 1\lor 3<x<5