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## Homework Statement

[itex]\frac{3x + 1}{2x - 6}[/itex] < 3

## Homework Equations

## The Attempt at a Solution

[itex]\frac{3x + 1}{2(x -3}[/itex] < 3

[itex]\frac{3x +1}{x - 3}[/itex] < 6

Assume x < 3

3x + 1 > 6(x - 3)

3x + 1 > 6x - 18

3x + 1 - 6x + 18 > 0

19 > 3x

x < 19/3

No Contradiction.

Assume x > 3

3x + 1 < 6x - 18

3x - 19 > 0

3x > 19

x > 19/3

No Contradiction

How do I know which set of values to take?