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

The solution to (x-2)/(3x+5) -5/3

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

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

x \leq - 2 or x > - \frac{5}{3}

Interval Notation

(- \infty, - 2] \cup (- \frac{5}{3}, \infty)

Decimal Notation

x \leq - 2 or x > - 1.66666 \dots

Solution steps

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

Rewrite in standard form

\frac{- 11 x - 22}{3 x + 5} \leq 0

Factor

\frac{- 11 x - 22}{3 x + 5} : \frac{- 11 ( x + 2 )}{3 x + 5}

\frac{- 11 ( x + 2 )}{3 x + 5} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 11 ( x + 2 ) ) ( - 1 )}{3 x + 5} \geq 0 \cdot (- 1)

Simplify

\frac{11 ( x + 2 )}{3 x + 5} \geq 0

Divide both sides by

11

\frac{\frac{11 ( x + 2 )}{3 x + 5}}{11} \geq \frac{0}{11}

Simplify

\frac{x + 2}{3 x + 5} \geq 0

Identify the intervals

x \leq - 2 or x > - \frac{5}{3}

- 5 x^{2} + 20 x = 0

\frac{m ^{5} + 3 m ^{4} - 2 m ^{3}}{2 m ^{3}}

x^{2} - 2 x y - 35 y^{2}

\frac{3 ( m ) ^{3}}{2 m ^{- 9}}

\frac{2}{3} (6 h - 9) = 6