0,5+0,2*x>0 inequation

Given the inequality:
$$\frac{x}{5} + \frac{1}{2} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{x}{5} + \frac{1}{2} = 0$$
Solve:
Given the linear equation:

(1/2)+(1/5)*x = 0

Expand brackets in the left part

1/2+1/5x = 0

Move free summands (without x)
from left part to right part, we given:
$$\frac{x}{5} = - \frac{1}{2}$$
Divide both parts of the equation by 1/5

x = -1/2 / (1/5)

$$x_{1} = - \frac{5}{2}$$
$$x_{1} = - \frac{5}{2}$$
This roots
$$x_{1} = - \frac{5}{2}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{5}{2} + - \frac{1}{10}$$
=
$$- \frac{13}{5}$$
substitute to the expression
$$\frac{x}{5} + \frac{1}{2} > 0$$
$$\frac{-13}{5 \cdot 5} + \frac{1}{2} > 0$$

-1/50 > 0

Then
$$x < - \frac{5}{2}$$
no execute
the solution of our inequality is:
$$x > - \frac{5}{2}$$

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