Question

How do you solve and write the following in interval notation: `( 2 x - 1 ) / ( x - 3 ) <1`?

Answer 1

`x in (-2, 3)`

Explanation:

`(2x-1)/(x-3)=2+5/(x-3) < 1`.

So, `5/(x-3) < -1`. And so, `LHS < 0 to x-3 < 0 to x < 3`

Cross multiply and reverse the inequality.

`5 > -(x-3) to x > -2`.

Thus, `-2 < x <3`