|8-4x|<8 inequation

Given the inequality:
$$\left|{8 - 4 x}\right| < 8$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{8 - 4 x}\right| = 8$$
Solve:
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.

1.
$$4 x - 8 \geq 0$$
or
$$2 \leq x \wedge x < \infty$$
we get the equation
$$\left(4 x - 8\right) - 8 = 0$$
after simplifying we get
$$4 x - 16 = 0$$
the solution in this interval:
$$x_{1} = 4$$

2.
$$4 x - 8 < 0$$
or
$$-\infty < x \wedge x < 2$$
we get the equation
$$\left(8 - 4 x\right) - 8 = 0$$
after simplifying we get
$$- 4 x = 0$$
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
$$\left|{8 - 4 x}\right| < 8$$
$$\left|{8 - \frac{\left(-1\right) 4}{10}}\right| < 8$$

42/5 < 8

but

42/5 > 8

Then
$$x < 0$$
no execute
one of the solutions of our inequality is:
$$x > 0 \wedge x < 4$$

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       x2      x1