What is (x-2)/(5x+1)<= 3/4 ?

The solution to (x-2)/(5x+1) -1/5

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(x-2)/(5x+1)<= 3/4

\frac{x - 2}{5 x + 1} \leq \frac{3}{4}

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

Interval Notation

(- \infty, - 1] \cup (- \frac{1}{5}, \infty)

Decimal Notation

x \leq - 1 or x > - 0.2

Solution steps

\frac{x - 2}{5 x + 1} \leq \frac{3}{4}

Rewrite in standard form

\frac{- 11 x - 11}{5 x + 1} \leq 0

Factor

\frac{- 11 x - 11}{5 x + 1} : \frac{- 11 ( x + 1 )}{5 x + 1}

\frac{- 11 ( x + 1 )}{5 x + 1} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 11 ( x + 1 ) ) ( - 1 )}{5 x + 1} \geq 0 \cdot (- 1)

Simplify

\frac{11 ( x + 1 )}{5 x + 1} \geq 0

Divide both sides by

11

\frac{\frac{11 ( x + 1 )}{5 x + 1}}{11} \geq \frac{0}{11}

Simplify

\frac{x + 1}{5 x + 1} \geq 0

Identify the intervals

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

(x - 3) (5 x + 2) = 0

\frac{( 0.99 ) ^{3} - 1}{( 0.99 ) - 1}

6 t^{3} + 3 t^{4} - 2 t^{5} - t^{6}

25 w^{2} - 60 w + 36

2 (x^{2} - 8) - 4 = - 8

What is (x-2)/(5x+1)<= 3/4 ?
The solution to (x-2)/(5x+1)<= 3/4 is x<=-1\lor x>-1/5