The question is , "Solve the inequality 2 - 3x < |x -3|" .

i tried it this way.

squaring both sides, ( 2 - 3x)² < (x - 3)²

8x² - 6x - 5 < 0

equating it to zero, 8x² - 6x - 5 = 0

critical values are, x = -0.5 x= 5/4

using these values, i did a sketch of the curve , and as i was required to find values of x which are < 0 , since 8x² - 6x - 5 < 0 , i got the range as -0.5 < x < 5/4

But the correct answer is x > = - 0.5 only. Why is 5/4 not accepted ?

Thnks in advance.