11-4*x<5 inequation

Given the inequality:
$$11 - 4 x < 5$$
To solve this inequality, we must first solve the corresponding equation:
$$11 - 4 x = 5$$
Solve:
Given the linear equation:

11-4*x = 5

Move free summands (without x)
from left part to right part, we given:
$$- 4 x = -6$$
Divide both parts of the equation by -4

x = -6 / (-4)

$$x_{1} = \frac{3}{2}$$
$$x_{1} = \frac{3}{2}$$
This roots
$$x_{1} = \frac{3}{2}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{3}{2}$$
=
$$\frac{7}{5}$$
substitute to the expression
$$11 - 4 x < 5$$
$$11 - \frac{4 \cdot 7}{5} < 5$$

27/5 < 5

but

27/5 > 5

Then
$$x < \frac{3}{2}$$
no execute
the solution of our inequality is:
$$x > \frac{3}{2}$$

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