SOLUTION: Solve the quadratic inequality by graphing an appropriate quadratic function. x^2+6x<-8

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Question 968149: Solve the quadratic inequality by graphing an appropriate quadratic function.
x^2+6x<-8
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B6x%3C-8
x%5E2%2B6x%2B8%3C0
%28x%2B4%29%28x%2B2%29%3C0

Critical numbers are -4 and -2

The critical numbers are not part of the solution.

Open circle those on a number line:

----------o-----o----------------
-7 -6 -5 -4 -3 -2 -1  0  1  2  3

Choose a test value left of -4, say -5

Substitute x=-5 in

%28x%2B4%29%28x%2B2%29%3C0
%28-5%2B4%29%28-5%2B2%29%3C0
%28-1%29%28-3%29%3C0
3%3C0

False so we do not shade the interval left of -4

----------o-----o----------------
-7 -6 -5 -4 -3 -2 -1  0  1  2  3

Choose a test value between of -4 and =-2, say -3

Substitute x=-3 in

%28x%2B4%29%28x%2B2%29%3C0
%28-3%2B4%29%28-3%2B2%29%3C0
%281%29%28-1%29%3C0
-1%3C0

True, so we do shade the interval between -4 and -2

----------o=====o----------------
-7 -6 -5 -4 -3 -2 -1  0  1  2  3

Choose a test value right of -4, say 0

Substitute x=0 in

%28x%2B4%29%28x%2B2%29%3C0
%280%2B4%29%280%2B2%29%3C0
%284%29%282%29%3C0
8%3C0

False so we do not shade the interval right of -2

So the set-builder notation is {x|-4 < x < -2}

So the interval notation of the graph is (-4,-2).

Edwin