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

The solution to ((2x+3))/((3x+2)) =-1/4

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((2x+3))/((3x+2))<= 2

\frac{( 2 x + 3 )}{( 3 x + 2 )} \leq 2

x < - \frac{2}{3} or x \geq - \frac{1}{4}

Interval Notation

(- \infty, - \frac{2}{3}) \cup [- \frac{1}{4}, \infty)

Decimal Notation

x < - 0.66666 \dots or x \geq - 0.25

Solution steps

\frac{2 x + 3}{3 x + 2} \leq 2

Rewrite in standard form

\frac{- 4 x - 1}{3 x + 2} \leq 0

Identify the intervals

x < - \frac{2}{3} or x \geq - \frac{1}{4}

x^{4} - 3 x^{2} + x^{2} + 3 x - 2 \geq 0

\frac{( 5 + x )}{( 12 - 3 x - x ^{2} )} \geq - 2

- x^{2} + x + 6 > 0

\frac{( x + 4 )}{( x - 2 )} - \frac{2}{( x + 1 )} < 0

\frac{( x + 2 )}{( x - 2 )} > 0

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