Nonlinear inequalities in one variable
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2x²+13x<18, 2x²+13x-18<0, x²+13x/2-9<0, x²+13x/2+169/16-169/16-9<0, (x+13/4)²-313/16<0.

(x+13/4)²-(√313/4)²<0, (x+13/4+√313/4)(x+13/4-√313/4)<0.

The product of the two bracketed factors must be negative so one must be positive and the other negative to get this result. So x lies between -13/4-√313/4 and -13/4+√313/4, that is -13/4-√313/4<x<-13/4+√313/4.

√313=17.6918 so -7.673<x<1.173 approx as illustrated below:

 

 

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