Question 1087723
.
<pre>
x*(x+1) > 112 -5x,      ====> (equivalent transformation)  ====>  

x^2 + x > 112 - 5x,     ====> (equivalent transformation)  ====>  

x^2 +x + 5x - 112 > 0,  ====> (equivalent transformation)  ====>  

x^2 + 6x - 112 > 0.


Factor left side. You will get

(x+14)*(x-8) > 0,  or,  equivalently

(x-(-14)*(x-8) > 0.    (1)


1)  If  x < -14  then each factor in the left side of (1) is negative,
    so the product is positive.


2)  If  -14 < x < 8  then the factor (x-(-14)) is positive, while the factor (x-8) in the left side of (1) is negative,
    so the product is negative.


3)  If 8 < x  then each factor in the left side of (1) is positive,
    so the product is positive.


<U>Answer</U>.  The given inequality has  the union of segments  ({{{-infinity}}},{{{-14}}}}}}] U [{{{8}}},{{{infinity}}}) as the solution set.
</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>".