If |2x - 3| < |x + 5| then x belongs to - 

Concept:

Comparison using inequality:

For any two real numbers \(a\) and \(b\) if \(\rm |a| < |b|\) then \(\rm a^2 < b^2\).

Calculation:

Use the given inequality and proceed as follows:

\(\rm|2x-3| < |x+5|\\ (2x-3)^2 < (x+5)^2\\ 4x^2+9-12x < x^2+25+10x\\ 3x^2-22x-16 < 0\\ 3x^2-24x+2x-16 < 0\\ 3x(x-8)+2(x-8) < 0\\ (3x+2)(x-8) < 0 \)

Therefore, we conclude that \(\left(-\dfrac{2}{3}, 8\right)\).