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

Jul 9, 2016

$x \in \left(- 2 , 3\right)$

#### Explanation:

$\frac{2 x - 1}{x - 3} = 2 + \frac{5}{x - 3} < 1$.

So, $\frac{5}{x - 3} < - 1$. And so, $L H S < 0 \to x - 3 < 0 \to x < 3$

Cross multiply and reverse the inequality.

$5 > - \left(x - 3\right) \to x > - 2$.

Thus, $- 2 < x < 3$