4+12x>0 inequation

Given the inequality:
$$12 x + 4 > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$12 x + 4 = 0$$
Solve:
Given the linear equation:

4+12*x = 0

Move free summands (without x)
from left part to right part, we given:
$$12 x = -4$$
Divide both parts of the equation by 12

x = -4 / (12)

$$x_{1} = - \frac{1}{3}$$
$$x_{1} = - \frac{1}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{3} + - \frac{1}{10}$$
=
$$- \frac{13}{30}$$
substitute to the expression
$$12 x + 4 > 0$$
$$\frac{\left(-13\right) 12}{30} + 4 > 0$$

-6/5 > 0

Then
$$x < - \frac{1}{3}$$
no execute
the solution of our inequality is:
$$x > - \frac{1}{3}$$

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