What is 1/(3x+2)< 1/(6x-1) ?

The solution to 1/(3x+2)< 1/(6x-1) is x<-2/3 \lor 1/6 <x<1

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1/(3x+2)< 1/(6x-1)

\frac{1}{3 x + 2} < \frac{1}{6 x - 1}

x < - \frac{2}{3} or \frac{1}{6} < x < 1

Interval Notation

(- \infty, - \frac{2}{3}) \cup (\frac{1}{6}, 1)

Decimal Notation

x < - 0.66666 \dots or 0.16666 \dots < x < 1

Solution steps

\frac{1}{3 x + 2} < \frac{1}{6 x - 1}

Rewrite in standard form

\frac{3 x - 3}{( 3 x + 2 ) ( 6 x - 1 )} < 0

Factor

\frac{3 x - 3}{( 3 x + 2 ) ( 6 x - 1 )} : \frac{3 ( x - 1 )}{( 3 x + 2 ) ( 6 x - 1 )}

\frac{3 ( x - 1 )}{( 3 x + 2 ) ( 6 x - 1 )} < 0

Divide both sides by

3

\frac{\frac{3 ( x - 1 )}{( 3 x + 2 ) ( 6 x - 1 )}}{3} < \frac{0}{3}

Simplify

\frac{x - 1}{( 3 x + 2 ) ( 6 x - 1 )} < 0

Identify the intervals

x < - \frac{2}{3} or \frac{1}{6} < x < 1

x^{2} + 3 > 4

\frac{x ( 3 - 4 x ) ( x + 1 )}{( 2 x - 5 )} < 0

\frac{x}{( x - 1 )} > \frac{1}{x}

(\frac{( x - x ^{2} )}{( x ^{2} + 2 x )}) \geq 0

\frac{x + 1}{x} > 2

What is 1/(3x+2)< 1/(6x-1) ?
The solution to 1/(3x+2)< 1/(6x-1) is x<-2/3 \lor 1/6 <x<1