# Solve the inequality and specify any excluded values? -2 < (3x+1)/(x-3)

Feb 28, 2017

$x > 1 , x \ne 3$

#### Explanation:

First, keep in mind that you need

$x - 3 \ne 0 \implies x \ne 3$

since $x = 3$ would make the denominator equal to $0$.

Now, multiply both sides by $x - 3$ to get

$- 2 \left(x - 3\right) < 3 x + 1$

Next, expand the brackets

$- 2 x + 6 < 3 x + 1$

Don't forget your rules for multiplying negatives!

Next, do some rearranging to get the $x$'s on one side and the other terms on the other side

$6 < 5 x + 1$

$5 < 5 x$

Therefore,

$1 < x \text{ }$ or $\text{ } x > 1$

I hope this helps.