Question

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

Answer 1

`x>1, x!=3`

Explanation:

First, keep in mind that you need

`x - 3 !=0 implies x !=3`

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

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

`-2(x-3) < 3x+1`

Next, expand the brackets

`-2x+6<3x+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 < 5x+1`

`5 < 5x`

Therefore,

`1 < x " "` or `" "x > 1`

I hope this helps.