7x-4(2x-1)≥-7 inequation

Given the inequality:
$$7 x - 4 \left(2 x - 1\right) \geq -7$$
To solve this inequality, we must first solve the corresponding equation:
$$7 x - 4 \left(2 x - 1\right) = -7$$
Solve:
Given the linear equation:

7*x-4*(2*x-1) = -7

Expand brackets in the left part

7*x-4*2*x+4*1 = -7

Looking for similar summands in the left part:

4 - x = -7

Move free summands (without x)
from left part to right part, we given:
$$- x = -11$$
Divide both parts of the equation by -1

x = -11 / (-1)

$$x_{1} = 11$$
$$x_{1} = 11$$
This roots
$$x_{1} = 11$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 11$$
=
$$\frac{109}{10}$$
substitute to the expression
$$7 x - 4 \left(2 x - 1\right) \geq -7$$
$$- 4 \left(-1 + \frac{2 \cdot 109}{10}\right) + \frac{7 \cdot 109}{10} \geq -7$$

-69       
---- >= -7
 10       

the solution of our inequality is:
$$x \leq 11$$

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