What is 1/(x-3)+2/(3x-24)>= 0 ?

The solution to 1/(x-3)+2/(3x-24)>= 0 is 3 8

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1/(x-3)+2/(3x-24)>= 0

\frac{1}{x - 3} + \frac{2}{3 x - 24} \geq 0

3 < x \leq 6 or x > 8

Interval Notation

(3, 6] \cup (8, \infty)

Solution steps

\frac{1}{x - 3} + \frac{2}{3 x - 24} \geq 0

Rewrite in standard form

\frac{5 x - 30}{( x - 3 ) ( x - 8 )} \geq 0

Factor

\frac{5 x - 30}{( x - 3 ) ( x - 8 )} : \frac{5 ( x - 6 )}{( x - 3 ) ( x - 8 )}

\frac{5 ( x - 6 )}{( x - 3 ) ( x - 8 )} \geq 0

Divide both sides by

5

\frac{\frac{5 ( x - 6 )}{( x - 3 ) ( x - 8 )}}{5} \geq \frac{0}{5}

Simplify

\frac{x - 6}{( x - 3 ) ( x - 8 )} \geq 0

Identify the intervals

3 < x \leq 6 or x > 8

∣ x - 7 ∣ = 4

3 x^{2} + 6 x - 42 = 0

3 (5 x - 4)^{2} + 7 = 61

8^{- \frac{1}{3}}

\frac{2}{3} t - \frac{2 t + 1}{9} > 12

What is 1/(x-3)+2/(3x-24)>= 0 ?
The solution to 1/(x-3)+2/(3x-24)>= 0 is 3<x<= 6\lor x>8