What is the solution to this inequality: $| 2x-3| > - | x+3|?$ By using graphical method, I am getting all real numbers..
Where am I wrong in graphical method? How to solve this using calculation?


Because absolute values are always positive we have
$$
\lvert 2x - 3 \rvert \geq 0 \geq -\lvert x + 3 \rvert
$$
for all values of $x$. Hence the only time $\lvert 2x - 3 \rvert > -\lvert x + 3 \rvert$ could potentially not hold is when both sides equal $0$. But $2x - 3 = 0$ if and only if $x = \frac{3}{2}$ and $x + 3 = 0$ if and only if $x = -3$ and clearly these cannot happen at the same time. Thus $\lvert 2x - 3 \rvert > -\lvert x + 3 \rvert$ holds for all values of $x$.
