24-3x>51 inequation

Given the inequality:
$$24 - 3 x > 51$$
To solve this inequality, we must first solve the corresponding equation:
$$24 - 3 x = 51$$
Solve:
Given the linear equation:

24-3*x = 51

Move free summands (without x)
from left part to right part, we given:
$$- 3 x = 27$$
Divide both parts of the equation by -3

x = 27 / (-3)

$$x_{1} = -9$$
$$x_{1} = -9$$
This roots
$$x_{1} = -9$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-9 + - \frac{1}{10}$$
=
$$- \frac{91}{10}$$
substitute to the expression
$$24 - 3 x > 51$$
$$24 - \frac{\left(-91\right) 3}{10} > 51$$

513     
--- > 51
 10     

the solution of our inequality is:
$$x < -9$$

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