What is (x-5)/(3x+7)<= 4 ?

The solution to (x-5)/(3x+7) -7/3

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(x-5)/(3x+7)<= 4

\frac{x - 5}{3 x + 7} \leq 4

x \leq - 3 or x > - \frac{7}{3}

Interval Notation

(- \infty, - 3] \cup (- \frac{7}{3}, \infty)

Decimal Notation

x \leq - 3 or x > - 2.33333 \dots

Solution steps

\frac{x - 5}{3 x + 7} \leq 4

Rewrite in standard form

\frac{- 11 x - 33}{3 x + 7} \leq 0

Factor

\frac{- 11 x - 33}{3 x + 7} : \frac{- 11 ( x + 3 )}{3 x + 7}

\frac{- 11 ( x + 3 )}{3 x + 7} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 11 ( x + 3 ) ) ( - 1 )}{3 x + 7} \geq 0 \cdot (- 1)

Simplify

\frac{11 ( x + 3 )}{3 x + 7} \geq 0

Divide both sides by

11

\frac{\frac{11 ( x + 3 )}{3 x + 7}}{11} \geq \frac{0}{11}

Simplify

\frac{x + 3}{3 x + 7} \geq 0

Identify the intervals

x \leq - 3 or x > - \frac{7}{3}

3 x \geq - 15

\frac{- 1}{3} - 1

(- 4 y^{3})^{2}

(2 x - 1) (3 x + 5) = 0

(5^{\frac{1}{3}})^{\frac{1}{3}}