Question

The solution set of x for the given inequality $|x+2|-|x-1|<x-\frac{3}{2}$, is

• A. $(-2,-\frac{3}{2})\cup (\frac{9}{2},\infty )$
• B. $(-2,-\frac{3}{2})\cup (-\frac{5}{2},-2)$
• C. $(\frac{9}{2},\infty )$
• D. None of these

Answer 1

The correct option is C $(\frac{9}{2},\infty )$


$\begin{array}{c}x<-2\\ Onsolvingx>\frac{-3}{2}\\ xϵ\varphi \end{array}|\begin{array}{c}-2<x<1\\ x<\frac{-5}{2}\\ xϵ\varphi \end{array}|\begin{array}{c}x>1\\ x>\frac{9}{2}\\ xϵ(\frac{9}{2},\infty )\end{array}|$