Absolute value inequality

Question

 

Can you please solve this question with steps and explanation is there any genergeneral and accurate way to solve such absolute value inequality

|x²-3x-15|<2x²-x

Answer 1

I Assuming the argument is positive

x² - 3x - 15 < 2x² - x

0 < x² + 2x + 15

ℜ

 

II Assuming the argument is negative (Not really necessary since all Reals solve the first

-(x² - 3x - 15) < 2x² - x

-x² + 3x + 15 < 2x² - x

0 < 3x² - 4x - 15

0 < (x - 3)(3x + 5)

x ∈ {x | x , -3 or x > 5/3}