Question 1087724: Solve the quadratic inequality. Write the solution set in interval notation. Show the complete solution.
𝑎2+3𝑎+2<−3(𝑎+2)
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! I will write it as
 , because I am assuming that that is what you meant.
To solve inequalities, we transform them into equivalent inequalities
(meaning inequalities that have exactly all the same solutions).
To do that it is always safe to add the same number or expression to both sides.
In this case, I found that factoring that quadratic polynomial from the start was easier for me.
That last inequality could also be written as  ,
but that is not needed in this case.
In fact, the factored form makes it easier to see the solution.
You know that the zeros of  are  ,
and that is where the sign changes for each factor, and for that quadratic polynomial.
In between those two zeros it is negative,
so the solution to is
 , or  .
That the quadratic polynomial is negative between -4 and -2 is obvioumany different ways.
Looking at the quadratic function/expression/polynomial  ,
you see that the leading coefficient is that invisible 
in the  leading term ,
so its graph opens up, and the polynomial is negative between the roots.
It is also obvious because is  for  ,
and since the polynomial changes sign for multiplicity 1 zeros a=-2, and, a=-4.
that would make it so that
 for  (including for a=0),
for , and
for  .
You could also look at the sign of each factor.
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