How do you solve the absolute value inequality #abs(2x + 1)< abs(3x - 2)#?
The inequality would hold good, even if we square both sides, but then absolute value sign would not be material, as both sides would be positive only. Accordingly,
Case1. Both factors are positive would mean x>3, x>1/5 . If x >3 , it automatically implies it is >1/5. It is ,therefore, concluded that x>3.
case2. Both factors are negative would mean x<1/5 , x<3. If x<1/5, it implies that it is <3. Hence conclusion is x<1/5.
Now x>3 and x<1/5 cannot happen at the same time. Hence there is no solution to the given inequality. If this is represented on the number line the conclusion would become more obvious.