5x+7 inequation

Given the inequality:
$$5 x + 7 > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$5 x + 7 = 0$$
Solve:
Given the linear equation:

5*x+7 = 0

Move free summands (without x)
from left part to right part, we given:
$$5 x = -7$$
Divide both parts of the equation by 5

x = -7 / (5)

$$x_{1} = - \frac{7}{5}$$
$$x_{1} = - \frac{7}{5}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{7}{5} + - \frac{1}{10}$$
=
$$- \frac{3}{2}$$
substitute to the expression
$$5 x + 7 > 0$$
$$\frac{\left(-3\right) 5}{2} + 7 > 0$$

-1/2 > 0

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

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