|×-2|>2 inequation

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

1.
$$x - 2 \geq 0$$
or
$$2 \leq x \wedge x < \infty$$
we get the equation
$$\left(x - 2\right) - 2 = 0$$
after simplifying we get
$$x - 4 = 0$$
the solution in this interval:
$$x_{1} = 4$$

2.
$$x - 2 < 0$$
or
$$-\infty < x \wedge x < 2$$
we get the equation
$$\left(2 - x\right) - 2 = 0$$
after simplifying we get
$$- x = 0$$
the solution in this interval:
$$x_{2} = 0$$


$$x_{1} = 4$$
$$x_{2} = 0$$
$$x_{1} = 4$$
$$x_{2} = 0$$
This roots
$$x_{2} = 0$$
$$x_{1} = 4$$
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
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$- \frac{1}{10}$$
=
$$- \frac{1}{10}$$
substitute to the expression
$$\left|{x - 2}\right| > 2$$
$$\left|{-2 + - \frac{1}{10}}\right| > 2$$

21    
-- > 2
10    

one of the solutions of our inequality is:
$$x < 0$$

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

Other solutions will get with the changeover to the next point
etc.
The answer:
$$x < 0$$
$$x > 4$$