7,2x>-27 inequation

Given the inequality:
$$\frac{36 x}{5} > -27$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{36 x}{5} = -27$$
Solve:
Given the linear equation:

(36/5)*x = -27

Expand brackets in the left part

36/5x = -27

Divide both parts of the equation by 36/5

x = -27 / (36/5)

$$x_{1} = - \frac{15}{4}$$
$$x_{1} = - \frac{15}{4}$$
This roots
$$x_{1} = - \frac{15}{4}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{15}{4} + - \frac{1}{10}$$
=
$$- \frac{77}{20}$$
substitute to the expression
$$\frac{36 x}{5} > -27$$
$$\frac{\left(-77\right) 36}{5 \cdot 20} > -27$$

-693       
----- > -27
  25       

Then
$$x < - \frac{15}{4}$$
no execute
the solution of our inequality is:
$$x > - \frac{15}{4}$$

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