3x+5/2x-7>0 inequation

Given the inequality:
$$\left(\frac{5 x}{2} + 3 x\right) - 7 > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(\frac{5 x}{2} + 3 x\right) - 7 = 0$$
Solve:
Given the linear equation:

3*x+5/2*x-7 = 0

Looking for similar summands in the left part:

-7 + 11*x/2 = 0

Move free summands (without x)
from left part to right part, we given:
$$\frac{11 x}{2} = 7$$
Divide both parts of the equation by 11/2

x = 7 / (11/2)

$$x_{1} = \frac{14}{11}$$
$$x_{1} = \frac{14}{11}$$
This roots
$$x_{1} = \frac{14}{11}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{14}{11}$$
=
$$\frac{129}{110}$$
substitute to the expression
$$\left(\frac{5 x}{2} + 3 x\right) - 7 > 0$$
$$-7 + \left(\frac{5 \cdot 129}{2 \cdot 110} + \frac{3 \cdot 129}{110}\right) > 0$$

-11     
---- > 0
 20     

Then
$$x < \frac{14}{11}$$
no execute
the solution of our inequality is:
$$x > \frac{14}{11}$$

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