Problem: Which of the following sets of x-values satisfy the inequality 2x2+x<6?
Answer Choices:
A. −2<x<23​
B. x>23​ or x<−2
C. x<23​
D. 23​<x<2
E. x<−2
Solution:
2x2+x<6,x2+2x​<3,x2+2x​+161​<3+161​, (x+41​)2<1649​,∣∣∣∣∣​x+41​∣∣∣∣∣​<47​, that is. x+41​<47​ and x+41​>−47​∴x<23​ and x>−2.