3-2x<5 inequation

Given the inequality:
$$3 - 2 x < 5$$
To solve this inequality, we must first solve the corresponding equation:
$$3 - 2 x = 5$$
Solve:
Given the linear equation:

3-2*x = 5

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

x = 2 / (-2)

$$x_{1} = -1$$
$$x_{1} = -1$$
This roots
$$x_{1} = -1$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-1 + - \frac{1}{10}$$
=
$$- \frac{11}{10}$$
substitute to the expression
$$3 - 2 x < 5$$
$$3 - \frac{\left(-11\right) 2}{10} < 5$$

26/5 < 5

but

26/5 > 5

Then
$$x < -1$$
no execute
the solution of our inequality is:
$$x > -1$$

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