11x-4-6x≥9-4x+5 inequation

Given the inequality:
$$- 6 x + 11 x - 4 \geq - 4 x + 5 + 9$$
To solve this inequality, we must first solve the corresponding equation:
$$- 6 x + 11 x - 4 = - 4 x + 5 + 9$$
Solve:
Given the linear equation:

11*x-4-6*x = 9-4*x+5

Looking for similar summands in the left part:

-4 + 5*x = 9-4*x+5

Looking for similar summands in the right part:

-4 + 5*x = 14 - 4*x

Move free summands (without x)
from left part to right part, we given:
$$5 x = - 4 x + 18$$
Move the summands with the unknown x
from the right part to the left part:
$$9 x = 18$$
Divide both parts of the equation by 9

x = 18 / (9)

$$x_{1} = 2$$
$$x_{1} = 2$$
This roots
$$x_{1} = 2$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 2$$
=
$$\frac{19}{10}$$
substitute to the expression
$$- 6 x + 11 x - 4 \geq - 4 x + 5 + 9$$
$$- \frac{6 \cdot 19}{10} - 4 + 11 \cdot \frac{19}{10} \geq - \frac{4 \cdot 19}{10} + 5 + 9$$

11/2 >= 32/5

but

11/2 < 32/5

Then
$$x \leq 2$$
no execute
the solution of our inequality is:
$$x \geq 2$$

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