113,4>−8,1x inequation

Given the inequality:
$$\frac{567}{5} > - \frac{81 x}{10}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{567}{5} = - \frac{81 x}{10}$$
Solve:
Given the linear equation:

(567/5) = -(81/10)*x

Expand brackets in the left part

567/5 = -(81/10)*x

Expand brackets in the right part

567/5 = -81/10x

Move free summands (without x)
from left part to right part, we given:
$$0 = - \frac{81 x}{10} - \frac{567}{5}$$
Move the summands with the unknown x
from the right part to the left part:
$$\frac{81 x}{10} = - \frac{567}{5}$$
Divide both parts of the equation by 81/10

x = -567/5 / (81/10)

$$x_{1} = -14$$
$$x_{1} = -14$$
This roots
$$x_{1} = -14$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-14 + - \frac{1}{10}$$
=
$$- \frac{141}{10}$$
substitute to the expression
$$\frac{567}{5} > - \frac{81 x}{10}$$
$$\frac{567}{5} > - \frac{\left(-141\right) 81}{10 \cdot 10}$$

        11421
567/5 > -----
         100 

Then
$$x < -14$$
no execute
the solution of our inequality is:
$$x > -14$$

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