|x-14|<=0.4 inequation

Given the inequality:
$$\left|{x - 14}\right| \leq \frac{2}{5}$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{x - 14}\right| = \frac{2}{5}$$
Solve:
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.

1.
$$x - 14 \geq 0$$
or
$$14 \leq x \wedge x < \infty$$
we get the equation
$$\left(x - 14\right) - \frac{2}{5} = 0$$
after simplifying we get
$$x - \frac{72}{5} = 0$$
the solution in this interval:
$$x_{1} = \frac{72}{5}$$

2.
$$x - 14 < 0$$
or
$$-\infty < x \wedge x < 14$$
we get the equation
$$\left(14 - x\right) - \frac{2}{5} = 0$$
after simplifying we get
$$\frac{68}{5} - x = 0$$
the solution in this interval:
$$x_{2} = \frac{68}{5}$$


$$x_{1} = \frac{72}{5}$$
$$x_{2} = \frac{68}{5}$$
$$x_{1} = \frac{72}{5}$$
$$x_{2} = \frac{68}{5}$$
This roots
$$x_{2} = \frac{68}{5}$$
$$x_{1} = \frac{72}{5}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{2}$$
For example, let's take the point
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{68}{5}$$
=
$$\frac{27}{2}$$
substitute to the expression
$$\left|{x - 14}\right| \leq \frac{2}{5}$$
$$\left|{-14 + \frac{27}{2}}\right| \leq \frac{2}{5}$$

1/2 <= 2/5

but

1/2 >= 2/5

Then
$$x \leq \frac{68}{5}$$
no execute
one of the solutions of our inequality is:
$$x \geq \frac{68}{5} \wedge x \leq \frac{72}{5}$$

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