What is (12x)/(x-4)>= (6x)/(x+6) ?

The solution to (12x)/(x-4)>= (6x)/(x+6) is x 4

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(12x)/(x-4)>= (6x)/(x+6)

\frac{12 x}{x - 4} \geq \frac{6 x}{x + 6}

x \leq - 16 or - 6 < x \leq 0 or x > 4

Interval Notation

(- \infty, - 16] \cup (- 6, 0] \cup (4, \infty)

Solution steps

\frac{12 x}{x - 4} \geq \frac{6 x}{x + 6}

Rewrite in standard form

\frac{6 x ^{2} + 96 x}{( x - 4 ) ( x + 6 )} \geq 0

Factor

\frac{6 x ^{2} + 96 x}{( x - 4 ) ( x + 6 )} : \frac{6 x ( x + 16 )}{( x - 4 ) ( x + 6 )}

\frac{6 x ( x + 16 )}{( x - 4 ) ( x + 6 )} \geq 0

Divide both sides by

6

\frac{\frac{6 x ( x + 16 )}{( x - 4 ) ( x + 6 )}}{6} \geq \frac{0}{6}

Simplify

\frac{x ( x + 16 )}{( x - 4 ) ( x + 6 )} \geq 0

Identify the intervals

x \leq - 16 or - 6 < x \leq 0 or x > 4

- 2 x^{2} + x - 1 < 0

x^{2} - 2 x < 1

x^{2} - 2 > 2 x + 1

(x + 2) \cdot x (x - 4) \leq 0

\frac{( x ^{2} - 3 x + 4 )}{( x + 5 )} < \frac{1}{3}

What is (12x)/(x-4)>= (6x)/(x+6) ?
The solution to (12x)/(x-4)>= (6x)/(x+6) is x<=-16\lor-6<x<= 0\lor x>4