What is (3x^2)/(7x+4)<-2 ?

The solution to (3x^2)/(7x+4)<-2 is x<-4\lor-2/3 <x<-4/7

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(3x^2)/(7x+4)<-2

\frac{3 x ^{2}}{7 x + 4} < - 2

x < - 4 or - \frac{2}{3} < x < - \frac{4}{7}

Interval Notation

(- \infty, - 4) \cup (- \frac{2}{3}, - \frac{4}{7})

Decimal Notation

x < - 4 or - 0.66666 \dots < x < - 0.57142 \dots

Solution steps

\frac{3 x ^{2}}{7 x + 4} < - 2

Rewrite in standard form

\frac{3 x ^{2} + 2 ( 7 x + 4 )}{7 x + 4} < 0

Factor

\frac{3 x ^{2} + 2 ( 7 x + 4 )}{7 x + 4} : \frac{( x + 4 ) ( 3 x + 2 )}{7 x + 4}

\frac{( x + 4 ) ( 3 x + 2 )}{7 x + 4} < 0

Identify the intervals

x < - 4 or - \frac{2}{3} < x < - \frac{4}{7}

4 u^{2} = 15 u + 4

- 6 \cdot \frac{5}{2}

\frac{1}{2} x = 2

5.182 3^{\frac{1}{100}} - 1

3 x^{2} - 10 x - 77

What is (3x^2)/(7x+4)<-2 ?
The solution to (3x^2)/(7x+4)<-2 is x<-4\lor-2/3 <x<-4/7