(6-5*x)/(4*x+5)>0 inequation

Given the inequality:
$$\frac{6 - 5 x}{4 x + 5} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{6 - 5 x}{4 x + 5} = 0$$
Solve:
Given the equation:
$$\frac{6 - 5 x}{4 x + 5} = 0$$
Multiply the equation sides by the denominator 5 + 4*x
we get:
$$6 - 5 x = 0$$
Move free summands (without x)
from left part to right part, we given:
$$- 5 x = -6$$
Divide both parts of the equation by -5

x = -6 / (-5)

$$x_{1} = \frac{6}{5}$$
$$x_{1} = \frac{6}{5}$$
This roots
$$x_{1} = \frac{6}{5}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{6}{5}$$
=
$$\frac{11}{10}$$
substitute to the expression
$$\frac{6 - 5 x}{4 x + 5} > 0$$
$$\frac{6 - \frac{5 \cdot 11}{10}}{\frac{4 \cdot 11}{10} + 5} > 0$$

5/94 > 0

the solution of our inequality is:
$$x < \frac{6}{5}$$

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