(x^2)-2*(|x|)<3 inequation

Given the inequality:
$$x^{2} - 2 \left|{x}\right| < 3$$
To solve this inequality, we must first solve the corresponding equation:
$$x^{2} - 2 \left|{x}\right| = 3$$
Solve:
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.

1.
$$x \geq 0$$
or
$$0 \leq x \wedge x < \infty$$
we get the equation
$$x^{2} - 2 x - 3 = 0$$
after simplifying we get
$$x^{2} - 2 x - 3 = 0$$
the solution in this interval:
$$x_{1} = -1$$
but x1 not in the inequality interval
$$x_{2} = 3$$

2.
$$x < 0$$
or
$$-\infty < x \wedge x < 0$$
we get the equation
$$x^{2} - 2 \left(- x\right) - 3 = 0$$
after simplifying we get
$$x^{2} + 2 x - 3 = 0$$
the solution in this interval:
$$x_{3} = -3$$
$$x_{4} = 1$$
but x4 not in the inequality interval


$$x_{1} = 3$$
$$x_{2} = -3$$
$$x_{1} = 3$$
$$x_{2} = -3$$
This roots
$$x_{2} = -3$$
$$x_{1} = 3$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{2}$$
For example, let's take the point
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$-3 + - \frac{1}{10}$$
=
$$- \frac{31}{10}$$
substitute to the expression
$$x^{2} - 2 \left|{x}\right| < 3$$
$$- 2 \left|{- \frac{31}{10}}\right| + \left(- \frac{31}{10}\right)^{2} < 3$$

341    
--- < 3
100    

but

341    
--- > 3
100    

Then
$$x < -3$$
no execute
one of the solutions of our inequality is:
$$x > -3 \wedge x < 3$$

         _____  
        /     \  
-------ο-------ο-------
       x2      x1