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

Question

1440 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-28T19:03:57

$x>1, x!=3$

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.

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