5x/2>7 inequation

Given the inequality:
$$\frac{5 x}{2} > 7$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{5 x}{2} = 7$$
Solve:
Given the linear equation:

5*x/2 = 7

Divide both parts of the equation by 5/2

x = 7 / (5/2)

$$x_{1} = \frac{14}{5}$$
$$x_{1} = \frac{14}{5}$$
This roots
$$x_{1} = \frac{14}{5}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{14}{5}$$
=
$$\frac{27}{10}$$
substitute to the expression
$$\frac{5 x}{2} > 7$$
$$5 \cdot \frac{27}{10} \cdot \frac{1}{2} > 7$$

27/4 > 7

Then
$$x < \frac{14}{5}$$
no execute
the solution of our inequality is:
$$x > \frac{14}{5}$$

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