Given the inequality:
$$- 6 x > 12$$
To solve this inequality, we must first solve the corresponding equation:
$$- 6 x = 12$$
Solve:
Given the linear equation:
-6*x = 12
Divide both parts of the equation by -6
x = 12 / (-6)
$$x_{1} = -2$$
$$x_{1} = -2$$
This roots
$$x_{1} = -2$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-2 + - \frac{1}{10}$$
=
$$- \frac{21}{10}$$
substitute to the expression
$$- 6 x > 12$$
$$- \frac{\left(-21\right) 6}{10} > 12$$
63/5 > 12
the solution of our inequality is:
$$x < -2$$
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