Question 1087737
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<pre>
{{{x^2+9x+13}}} > {{{-7}}}  ---->  (add 7 to both sides)  ---->

{{{x^2+9x+20}}} > {{{0}}}   ---->  (factor left side)  ---->


(x+5)*(x+4) > 0,   or,  equivalently,

(x - (-5)*(x - (-4)) > 0.


1)  x < -5  ====>  both factors in the left are negative; hence, the product is positive.


2)  -5 < x < -4  ====>  factor (x - (-5)) in the left is positive while factor (x - (-4)) in the left is positive; hence, the product is negative.


3)  x > -4  ====>  both factors in the left are positive; hence, the product is positive.


<U>Answer</U>. The solution is the union of two intervals ({{{-infinity}}},{{{-5}}}) U ({{{-4}}},{{{infinity}}}).
</pre>

Solved.



If you want to learn on how to solve quadratic inequalities, read the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Inequalities/Solving-problems-on-quadratic-inequalities.lesson>Solving problems on quadratic inequalities</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic "<U>Inequalities</U>".