3*x-4*(2*x-8)<-3 inequation

Given the inequality:
$$3 x - 4 \left(2 x - 8\right) < -3$$
To solve this inequality, we must first solve the corresponding equation:
$$3 x - 4 \left(2 x - 8\right) = -3$$
Solve:
Given the linear equation:

3*x-4*(2*x-8) = -3

Expand brackets in the left part

3*x-4*2*x+4*8 = -3

Looking for similar summands in the left part:

32 - 5*x = -3

Move free summands (without x)
from left part to right part, we given:
$$- 5 x = -35$$
Divide both parts of the equation by -5

x = -35 / (-5)

$$x_{1} = 7$$
$$x_{1} = 7$$
This roots
$$x_{1} = 7$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 7$$
=
$$\frac{69}{10}$$
substitute to the expression
$$3 x - 4 \left(2 x - 8\right) < -3$$
$$- 4 \left(-8 + \frac{2 \cdot 69}{10}\right) + \frac{3 \cdot 69}{10} < -3$$

-5/2 < -3

but

-5/2 > -3

Then
$$x < 7$$
no execute
the solution of our inequality is:
$$x > 7$$

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