What is 4/(3x+1)<= 2/(x-4) ?

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4/(3x+1)<= 2/(x-4)

\frac{4}{3 x + 1} \leq \frac{2}{x - 4}

- 9 \leq x < - \frac{1}{3} or x > 4

Interval Notation

[- 9, - \frac{1}{3}) \cup (4, \infty)

Decimal Notation

- 9 \leq x < - 0.33333 \dots or x > 4

Solution steps

\frac{4}{3 x + 1} \leq \frac{2}{x - 4}

Rewrite in standard form

\frac{- 2 x - 18}{( x - 4 ) ( 3 x + 1 )} \leq 0

Factor

\frac{- 2 x - 18}{( x - 4 ) ( 3 x + 1 )} : \frac{- 2 ( x + 9 )}{( x - 4 ) ( 3 x + 1 )}

\frac{- 2 ( x + 9 )}{( x - 4 ) ( 3 x + 1 )} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 2 ( x + 9 ) ) ( - 1 )}{( x - 4 ) ( 3 x + 1 )} \geq 0 \cdot (- 1)

Simplify

\frac{2 ( x + 9 )}{( x - 4 ) ( 3 x + 1 )} \geq 0

Divide both sides by

2

\frac{\frac{2 ( x + 9 )}{( x - 4 ) ( 3 x + 1 )}}{2} \geq \frac{0}{2}

Simplify

\frac{x + 9}{( x - 4 ) ( 3 x + 1 )} \geq 0

Identify the intervals

- 9 \leq x < - \frac{1}{3} or x > 4

\frac{- 6}{i}

- 5 n - 3 n = - 8

64 p^{2} - 96 p + 36 - 16 q^{2}

\frac{4 y}{2 x ^{4} y}

What is 4/(3x+1)<= 2/(x-4) ?
The solution to 4/(3x+1)<= 2/(x-4) is -9<= x<-1/3 \lor x>4