|-x+2|<4 inequation

Given the inequality:
$$\left|{2 - x}\right| < 4$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{2 - x}\right| = 4$$
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
$$\left(x - 2\right) - 4 = 0$$
after simplifying we get
$$x - 6 = 0$$
the solution in this interval:
$$x_{1} = 6$$

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


$$x_{1} = 6$$
$$x_{2} = -2$$
$$x_{1} = 6$$
$$x_{2} = -2$$
This roots
$$x_{2} = -2$$
$$x_{1} = 6$$
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
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$-2 + - \frac{1}{10}$$
=
$$- \frac{21}{10}$$
substitute to the expression
$$\left|{2 - x}\right| < 4$$
$$\left|{2 - - \frac{21}{10}}\right| < 4$$

41    
-- < 4
10    

but

41    
-- > 4
10    

Then
$$x < -2$$
no execute
one of the solutions of our inequality is:
$$x > -2 \wedge x < 6$$

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