11-4x>6-6 inequation

Given the inequality:
$$11 - 4 x > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$11 - 4 x = 0$$
Solve:
Given the linear equation:

11-4*x = 6-6

Looking for similar summands in the right part:

11 - 4*x = 0

Move free summands (without x)
from left part to right part, we given:
$$- 4 x = -11$$
Divide both parts of the equation by -4

x = -11 / (-4)

$$x_{1} = \frac{11}{4}$$
$$x_{1} = \frac{11}{4}$$
This roots
$$x_{1} = \frac{11}{4}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{11}{4}$$
=
$$\frac{53}{20}$$
substitute to the expression
$$11 - 4 x > 0$$
$$11 - \frac{4 \cdot 53}{20} > 0$$

2/5 > 0

the solution of our inequality is:
$$x < \frac{11}{4}$$

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