4x−19≥1. inequation

Given the inequality:
$$4 x - 19 \geq 1$$
To solve this inequality, we must first solve the corresponding equation:
$$4 x - 19 = 1$$
Solve:
Given the linear equation:

4*x-19 = 1

Move free summands (without x)
from left part to right part, we given:
$$4 x = 20$$
Divide both parts of the equation by 4

x = 20 / (4)

$$x_{1} = 5$$
$$x_{1} = 5$$
This roots
$$x_{1} = 5$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 5$$
=
$$\frac{49}{10}$$
substitute to the expression
$$4 x - 19 \geq 1$$
$$-19 + \frac{4 \cdot 49}{10} \geq 1$$

3/5 >= 1

but

3/5 < 1

Then
$$x \leq 5$$
no execute
the solution of our inequality is:
$$x \geq 5$$

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