5-6*x>=0 inequation

Given the inequality:
$$5 - 6 x \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$5 - 6 x = 0$$
Solve:
Given the linear equation:

5-6*x = 0

Move free summands (without x)
from left part to right part, we given:
$$- 6 x = -5$$
Divide both parts of the equation by -6

x = -5 / (-6)

$$x_{1} = \frac{5}{6}$$
$$x_{1} = \frac{5}{6}$$
This roots
$$x_{1} = \frac{5}{6}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{5}{6}$$
=
$$\frac{11}{15}$$
substitute to the expression
$$5 - 6 x \geq 0$$
$$5 - \frac{6 \cdot 11}{15} \geq 0$$

3/5 >= 0

the solution of our inequality is:
$$x \leq \frac{5}{6}$$

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