SOLUTION: List the critical values of the related function. Then solve the inequality. x+11/x+2<8 i got -2,-5/7,(-&#8734;,-2)U(-5/7,&#8734;)

Algebra ->  Radicals -> SOLUTION: List the critical values of the related function. Then solve the inequality. x+11/x+2<8 i got -2,-5/7,(-&#8734;,-2)U(-5/7,&#8734;)      Log On


   

Question 922858: List the critical values of the related function. Then solve the inequality.
x+11/x+2<8
i got -2,-5/7,(-∞,-2)U(-5/7,∞)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
One would expect you really mean this:
(x+11)/(x+2)<8, in pure text.
%28x%2B11%29%2F%28x%2B2%29%3C8


The left member would be the expression defining the related function, and the critical points are its roots and any x values which make the function undefined. Accordingly, the critical values are -11 and -2.

Critical Values of x: -11 and -2.

SOLVING THE EQUATION:
%28x%2B11%29%2F%28x%2B2%29-8%3C0
%28x%2B11%29%2F%28x%2B2%29-8%28x%2B11%29%2F%28x%2B2%29%3C0
%28x%2B11-8x-88%29%2F%28x%2B2%29%3C0
%28-7x-77%29%2F%28x%2B2%29%3C0
%287x%2B77%29%2F%28x%2B2%29%3E0
Again, examing for critical values of x, they still are -2 and -11.

Three intervals to check.

x%3C-11:
%287%2A%28-12%29%2B77%29%2F%28-12%2B2%29=%28-something%29%2F%28-someelse%29%3E0 true.
-
-11%3Cx%3C-2:
%287%28-5%29%2B77%29%2F%28-5%2B2%29=%28something%29%2F%28-something%29%3E0 false.
-
x%3E-2:
%287%2A0%2B77%29%2F%280%2B2%29=77%2F2%3E0 true.


SOLUTIONS: (-infinity,-11) OR (-2, infinity)

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

List the critical values of the related function. Then solve the inequality.
x+11/x+2<8
i got -2,-5/7,(-∞,-2)U(-5/7,∞)


You are absolutely CORRECT!! Great job!!

The critical values are indeed - 2 and -+5%2F7, and the intervals that satisfy the inequality are INDEED

highlight_green%28x+%3C+-+2%29, and highlight_green%28x+%3E+-+5%2F7%29, which you correctly denoted in interval notation, CORRECTLY indicating that the

critical values, -+2 and -+5%2F7 are NOT PART of the solution.

Again, great job!!