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;)

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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)   (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.



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:





Again, examing for critical values of x, they still are -2 and -11.

Three intervals to check.

:
true.
-
:
false.
-
:
true.


SOLUTIONS: (,-11) OR (-2, )
Answer by MathTherapy(10552)   (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 , and the intervals that satisfy the inequality are INDEED

, and , which you correctly denoted in interval notation, CORRECTLY indicating that the

critical values,  and  are NOT PART of the solution.

Again, great job!! 

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