(5x-7)/4>0 inequation

Given the inequality:
$$\frac{5 x - 7}{4} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{5 x - 7}{4} = 0$$
Solve:
Given the linear equation:

(5*x-7)/4 = 0

Expand brackets in the left part

5*x/4-7/4 = 0

Move free summands (without x)
from left part to right part, we given:
$$\frac{5 x}{4} = \frac{7}{4}$$
Divide both parts of the equation by 5/4

x = 7/4 / (5/4)

$$x_{1} = \frac{7}{5}$$
$$x_{1} = \frac{7}{5}$$
This roots
$$x_{1} = \frac{7}{5}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{7}{5}$$
=
$$\frac{13}{10}$$
substitute to the expression
$$\frac{5 x - 7}{4} > 0$$
$$\frac{-7 + \frac{5 \cdot 13}{10}}{4} > 0$$

-1/8 > 0

Then
$$x < \frac{7}{5}$$
no execute
the solution of our inequality is:
$$x > \frac{7}{5}$$

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