What is ((3x-1))/((2x-4))<1 ?

The solution to ((3x-1))/((2x-4))<1 is -3<x<2

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((3x-1))/((2x-4))<1

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

- 3 < x < 2

Interval Notation

(- 3, 2)

Solution steps

\frac{3 x - 1}{2 x - 4} < 1

Rewrite in standard form

\frac{x + 3}{2 x - 4} < 0

Factor

\frac{x + 3}{2 x - 4} : \frac{x + 3}{2 ( x - 2 )}

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

Multiply both sides by

2

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

Simplify

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

Identify the intervals

- 3 < x < 2

\frac{( 8 x ^{2} + 16 x - 51 )}{( ( 2 x - 3 ) ( x + 4 ) )} < 3

\frac{1}{( x + 1 )} \geq \frac{2}{( x + 2 )}

\frac{( 2 x - x ^{2} + 11 )}{( x ^{2} + 2 x + 3 )} \geq 1

\frac{( 2 x - 1 )}{( x ^{3} + 2 x + x )} > 0

\frac{( ( n + 5 ) ( n - 9 ) )}{( n - 12 )} \geq 0