What is 3/(5x+1)<= 1/(x-3) ?

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3/(5x+1)<= 1/(x-3)

\frac{3}{5 x + 1} \leq \frac{1}{x - 3}

- 5 \leq x < - \frac{1}{5} or x > 3

Solution steps

\frac{3}{5 x + 1} \leq \frac{1}{x - 3}

Rewrite in standard form

\frac{- 2 x - 10}{( x - 3 ) ( 5 x + 1 )} \leq 0

Factor

\frac{- 2 x - 10}{( x - 3 ) ( 5 x + 1 )} : \frac{- 2 ( x + 5 )}{( x - 3 ) ( 5 x + 1 )}

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

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 2 ( x + 5 ) ) ( - 1 )}{( x - 3 ) ( 5 x + 1 )} \geq 0 \cdot (- 1)

Simplify

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

Divide both sides by

2

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

Simplify

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

Identify the intervals

- 5 \leq x < - \frac{1}{5} or x > 3

x - 24 \geq 9

- 310 x + 110 > - 12 x + 110

\frac{5 x - 6}{x - 6} \geq 0

\frac{7 + 2}{7 - 2}

3 x + 2 = 8

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