Given the inequality:
$$- 3 x > -12$$
To solve this inequality, we must first solve the corresponding equation:
$$- 3 x = -12$$
Solve:
Given the linear equation:
-3*x = -12
Divide both parts of the equation by -3
x = -12 / (-3)
$$x_{1} = 4$$
$$x_{1} = 4$$
This roots
$$x_{1} = 4$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 4$$
=
$$\frac{39}{10}$$
substitute to the expression
$$- 3 x > -12$$
$$- \frac{3 \cdot 39}{10} > -12$$
-117
----- > -12
10
the solution of our inequality is:
$$x < 4$$
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