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

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

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

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

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

Interval Notation

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

Decimal Notation

x < 1 or 1.5 < x < 3

Solution steps

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

Rewrite in standard form

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

Identify the intervals

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

3 x (x - 5) - 13 > 3 x^{2} - 2 x

3 x - 10 - 2 x^{2} < 0

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

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

(x - 1)^{2} < 25

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