What is ((3x-2))/((2x-3))<3 ?

The solution to ((3x-2))/((2x-3)) 7/3

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((3x-2))/((2x-3))<3

\frac{( 3 x - 2 )}{( 2 x - 3 )} < 3

x < \frac{3}{2} or x > \frac{7}{3}

Interval Notation

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

Decimal Notation

x < 1.5 or x > 2.33333 \dots

Solution steps

\frac{3 x - 2}{2 x - 3} < 3

Rewrite in standard form

\frac{- 3 x + 7}{2 x - 3} < 0

Identify the intervals

x < \frac{3}{2} or x > \frac{7}{3}

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

3 x^{2} - 8 x + 2 < 0

x (x - 1) (x - 2) (x - 3) > 0

x^{5} - 7 x^{4} + 13 x^{3} - x^{2} - 14 x + 8 \leq 0

\frac{x}{( x ^{2} - 3 x - 4 )} > 0

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