Nonlinear inequalities in one variable

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:

- All categories
- Pre-Algebra Answers 12.3k
- Algebra 1 Answers 25.3k
- Algebra 2 Answers 10.5k
- Geometry Answers 5.2k
- Trigonometry Answers 2.6k
- Calculus Answers 6.1k
- Statistics Answers 3k
- Word Problem Answers 10.2k
- Other Math Topics 6.7k

81,951 questions

86,346 answers

2,238 comments

71,626 users