What is ((3x+5))/((2x+1))<= 3 ?

The solution to ((3x+5))/((2x+1)) = 2/3

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((3x+5))/((2x+1))<= 3

\frac{( 3 x + 5 )}{( 2 x + 1 )} \leq 3

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

Interval Notation

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

Decimal Notation

x < - 0.5 or x \geq 0.66666 \dots

Solution steps

\frac{3 x + 5}{2 x + 1} \leq 3

Rewrite in standard form

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

Identify the intervals

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

\frac{1}{( 3 + 2 x - x ^{2} )} x < 3

\frac{( ( x - 9 ) ( x - 15 ) )}{( x - 12 )} \geq 0

\frac{6}{( 2 x + 3 )} < 0

\frac{x ^{2} + 1}{x} \geq 2

n^{2} \leq 4

What is ((3x+5))/((2x+1))<= 3 ?
The solution to ((3x+5))/((2x+1))<= 3 is x<-1/2 \lor x>= 2/3