SOLUTION: I need help with this inequality 6/(x-3)< 3/(x+1). Please show all work. Thank you.

Algebra ->  Inequalities -> SOLUTION: I need help with this inequality 6/(x-3)< 3/(x+1). Please show all work. Thank you.       Log On


   

Question 970061: I need help with this inequality 6/(x-3)< 3/(x+1). Please show all work. Thank you.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
6%2F%28x-3%29%3C+3%2F%28x%2B1%29

6%2F%28x-3%29-3%2F%28x%2B1%29%3C0

2%2F%28x-3%29-1%2F%28x%2B1%29%3C0

%282%28x%2B1%29-%28x-3%29%29%2F%28%28x-3%29%28x%2B1%29%29%3C0

%282x%2B2-x%2B3%29%2F%28%28x-3%29%28x%2B1%29%29%3C0

highlight%28%28x%2B5%29%2F%28%28x-3%29%28x%2B1%29%29%3C0%29
Critical values of x are -5,-1,3.
These make four intervals on the x-axis number line. Pick any value INSIDE each interval and check for truth or falseness for the inequality statement.

The intervals within to check are these:
x%3C-5
-
-5%3Cx%3C-1
-
-1%3Cx%3C3
-
3%3Cx