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

The solution to 4/(x-3)<= 2/(x+5) is x<=-13\lor-5<x<3

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

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

x \leq - 13 or - 5 < x < 3

Interval Notation

(- \infty, - 13] \cup (- 5, 3)

Solution steps

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

Rewrite in standard form

\frac{2 x + 26}{( x - 3 ) ( x + 5 )} \leq 0

Factor

\frac{2 x + 26}{( x - 3 ) ( x + 5 )} : \frac{2 ( x + 13 )}{( x - 3 ) ( x + 5 )}

\frac{2 ( x + 13 )}{( x - 3 ) ( x + 5 )} \leq 0

Divide both sides by

2

\frac{\frac{2 ( x + 13 )}{( x - 3 ) ( x + 5 )}}{2} \leq \frac{0}{2}

Simplify

\frac{x + 13}{( x - 3 ) ( x + 5 )} \leq 0

Identify the intervals

x \leq - 13 or - 5 < x < 3

\frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64}

5 x^{3} - 15 x^{2} + 10 x

∣ x + 2 ∣ > 1

\frac{( 4 m ^{3} ) ( 6 m ^{4} )}{3 m ^{2}}

2 x^{2} - 5 x = - 10

What is 4/(x-3)<= 2/(x+5) ?
The solution to 4/(x-3)<= 2/(x+5) is x<=-13\lor-5<x<3