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.