21+7*x>0 inequation

Given the inequality:
$$7 x + 21 > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$7 x + 21 = 0$$
Solve:
Given the linear equation:

21+7*x = 0

Move free summands (without x)
from left part to right part, we given:
$$7 x = -21$$
Divide both parts of the equation by 7

x = -21 / (7)

$$x_{1} = -3$$
$$x_{1} = -3$$
This roots
$$x_{1} = -3$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-3 + - \frac{1}{10}$$
=
$$- \frac{31}{10}$$
substitute to the expression
$$7 x + 21 > 0$$
$$\frac{\left(-31\right) 7}{10} + 21 > 0$$

-7/10 > 0

Then
$$x < -3$$
no execute
the solution of our inequality is:
$$x > -3$$

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