How to Solve Rational Inequalities?

[priscilla98]

Homework Statement

Solve (x+2)/(x+1) -2 < 0

Homework Equations

LCD: x + 1

The Attempt at a Solution

(x+2-2x-2)/(x+1) < 0

(-x )/(x+1) < 0

But somehow, I got the wrong answer. The answer is (4, 7]. But I don't know where I went wrong.

 

[priscilla98]

I tried everything I could to answer this problem. Am i right that the lcd is x + 1? Because when i multiply - 2 by x + 1, i end up having to cross out + 2 and -2.

 

[eumyang]

I'm confused because you title this thread "Absolute Value Inequalities," but your problem does not have any absolute value symbols. Can you double check the problem, please? Is the problem this?
$$\frac{x+2}{x+1} -2 < 0$$
Because that's what I'm interpreting.

Furthermore, according to WolframAlpha, the solution to what I typed above is
(-∞, -1) U (0, ∞), not (4, 7].69

 

[priscilla98]

Your right, its not absolute inequalities. It's rational equalities.

Okay, thanks a lot for answering this question. I really do appreciate it.