SOLUTION: Solve {{{x^3+2x^2-11x-12<0}}}

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Question 135536: Solve x%5E3%2B2x%5E2-11x-12%3C0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E3%2B2x%5E2-11x-12=0 Set the left side equal to zero.


When we use a graphing calculator, we find that the solutions are x=-4, x=-1 and x=3. So that means that the inequality x%5E3%2B2x%5E2-11x-12%3C0 factors to %28x%2B4%29%28x%2B1%29%28x-3%29%3C0




Now plot the critical values on a number line

number_line%28+600%2C+-10%2C+10%2C+-4%2C-1%2C3+%29



So let's evaluate a point that is to the left of (which is the left most endpoint). Let's evaluate the value x=-5

Start with the given inequality

Plug in x=-5

Evaluate and simplify



Since is true, this means that one part of the solution in interval notation is
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Now let's test a point that is in between the critical values and


Start with the given inequality

Plug in x=-2

Evaluate and simplify


Since is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored.
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Now let's test a point that is in between the critical values and


Start with the given inequality

Plug in x=1

Evaluate and simplify



Since is true, this means that one part of the solution in interval notation is
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So let's evaluate a point that is to the right of (which is the right most endpoint). Let's evaluate the value x=4

Start with the given inequality

Plug in x=4

Evaluate and simplify


Since is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored.
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Answer:
So the solution set in interval notation is