-12x+4x>=3-4 inequation

Given the inequality:
$$- 12 x + 4 x \geq -1$$
To solve this inequality, we must first solve the corresponding equation:
$$- 12 x + 4 x = -1$$
Solve:
Given the linear equation:

-12*x+4*x = 3-4

Looking for similar summands in the left part:

-8*x = 3-4

Looking for similar summands in the right part:

-8*x = -1

Divide both parts of the equation by -8

x = -1 / (-8)

$$x_{1} = \frac{1}{8}$$
$$x_{1} = \frac{1}{8}$$
This roots
$$x_{1} = \frac{1}{8}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{1}{8}$$
=
$$\frac{1}{40}$$
substitute to the expression
$$- 12 x + 4 x \geq -1$$
$$- \frac{12}{40} + \frac{4}{40} \geq -1$$

-1/5 >= -1

the solution of our inequality is:
$$x \leq \frac{1}{8}$$

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