3*x+5<9 inequation

Given the inequality:
$$3 x + 5 < 9$$
To solve this inequality, we must first solve the corresponding equation:
$$3 x + 5 = 9$$
Solve:
Given the linear equation:

3*x+5 = 9

Move free summands (without x)
from left part to right part, we given:
$$3 x = 4$$
Divide both parts of the equation by 3

x = 4 / (3)

$$x_{1} = \frac{4}{3}$$
$$x_{1} = \frac{4}{3}$$
This roots
$$x_{1} = \frac{4}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{4}{3}$$
=
$$\frac{37}{30}$$
substitute to the expression
$$3 x + 5 < 9$$
$$\frac{3 \cdot 37}{30} + 5 < 9$$

87    
-- < 9
10    

the solution of our inequality is:
$$x < \frac{4}{3}$$

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