-3x+6>5 inequation

Given the inequality:
$$6 - 3 x > 5$$
To solve this inequality, we must first solve the corresponding equation:
$$6 - 3 x = 5$$
Solve:
Given the linear equation:

-3*x+6 = 5

Move free summands (without x)
from left part to right part, we given:
$$- 3 x = -1$$
Divide both parts of the equation by -3

x = -1 / (-3)

$$x_{1} = \frac{1}{3}$$
$$x_{1} = \frac{1}{3}$$
This roots
$$x_{1} = \frac{1}{3}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{1}{3}$$
=
$$\frac{7}{30}$$
substitute to the expression
$$6 - 3 x > 5$$
$$6 - \frac{3 \cdot 7}{30} > 5$$

53    
-- > 5
10    

the solution of our inequality is:
$$x < \frac{1}{3}$$

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