27x>=12 inequation

Given the inequality:
$$27 x \geq 12$$
To solve this inequality, we must first solve the corresponding equation:
$$27 x = 12$$
Solve:
Given the linear equation:

27*x = 12

Divide both parts of the equation by 27

x = 12 / (27)

$$x_{1} = \frac{4}{9}$$
$$x_{1} = \frac{4}{9}$$
This roots
$$x_{1} = \frac{4}{9}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{4}{9}$$
=
$$\frac{31}{90}$$
substitute to the expression
$$27 x \geq 12$$
$$\frac{27 \cdot 31}{90} \geq 12$$

93      
-- >= 12
10      

but

93     
-- < 12
10     

Then
$$x \leq \frac{4}{9}$$
no execute
the solution of our inequality is:
$$x \geq \frac{4}{9}$$

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