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

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

Interval Notation

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

Decimal Notation

x < 1 or 1.5 < x \leq 3

Solution steps

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

Rewrite in standard form

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

Identify the intervals

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

(x - 1) (x - 5) (x - 15) \leq 0, (x - 3) (x - 10) > 0

[x + 6] > 4

\frac{( x + 5 ) ( x - 9 )}{( x - 12 )} > 0

(x^{2} - 4) (x^{3} - 5 x^{2} + 6 x) \geq 0

x^{3} - 6 x^{2} + 11 x - 6 < 0

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