What is (x-4)/(4x+7)<= 6 ?

The solution to (x-4)/(4x+7) -7/4

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(x-4)/(4x+7)<= 6

\frac{x - 4}{4 x + 7} \leq 6

x \leq - 2 or x > - \frac{7}{4}

Interval Notation

(- \infty, - 2] \cup (- \frac{7}{4}, \infty)

Decimal Notation

x \leq - 2 or x > - 1.75

Solution steps

\frac{x - 4}{4 x + 7} \leq 6

Rewrite in standard form

\frac{- 23 x - 46}{4 x + 7} \leq 0

Factor

\frac{- 23 x - 46}{4 x + 7} : \frac{- 23 ( x + 2 )}{4 x + 7}

\frac{- 23 ( x + 2 )}{4 x + 7} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 23 ( x + 2 ) ) ( - 1 )}{4 x + 7} \geq 0 \cdot (- 1)

Simplify

\frac{23 ( x + 2 )}{4 x + 7} \geq 0

Divide both sides by

23

\frac{\frac{23 ( x + 2 )}{4 x + 7}}{23} \geq \frac{0}{23}

Simplify

\frac{x + 2}{4 x + 7} \geq 0

Identify the intervals

x \leq - 2 or x > - \frac{7}{4}

x^{3} - 7 x^{2} + 16 x - 12

x^{4} - x^{3} - 3 x^{2} + 5 x - 2

\frac{( 3 + 3 i ) ( 4 - 2 i )}{2 - 2 i}

∣ 3 x - 5 ∣ \leq 4

3 x - 2 < 7