4x+5>3 inequation

Given the inequality:
$$4 x + 5 > 3$$
To solve this inequality, we must first solve the corresponding equation:
$$4 x + 5 = 3$$
Solve:
Given the linear equation:

4*x+5 = 3

Move free summands (without x)
from left part to right part, we given:
$$4 x = -2$$
Divide both parts of the equation by 4

x = -2 / (4)

$$x_{1} = - \frac{1}{2}$$
$$x_{1} = - \frac{1}{2}$$
This roots
$$x_{1} = - \frac{1}{2}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{2} + - \frac{1}{10}$$
=
$$- \frac{3}{5}$$
substitute to the expression
$$4 x + 5 > 3$$
$$\frac{\left(-3\right) 4}{5} + 5 > 3$$

13/5 > 3

Then
$$x < - \frac{1}{2}$$
no execute
the solution of our inequality is:
$$x > - \frac{1}{2}$$

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