4x+2:2-5x<1 inequation

Given the inequality:
$$- 5 x + \left(4 x + 1\right) < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$- 5 x + \left(4 x + 1\right) = 1$$
Solve:
Given the linear equation:

4*x+2/2-5*x = 1

Looking for similar summands in the left part:

1 - x = 1

Move free summands (without x)
from left part to right part, we given:
$$- x = 0$$
Divide both parts of the equation by -1

x = 0 / (-1)

$$x_{1} = 0$$
$$x_{1} = 0$$
This roots
$$x_{1} = 0$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10}$$
=
$$- \frac{1}{10}$$
substitute to the expression
$$- 5 x + \left(4 x + 1\right) < 1$$
$$- \frac{\left(-1\right) 5}{10} + \left(\frac{\left(-1\right) 4}{10} + 1\right) < 1$$

11    
-- < 1
10    

but

11    
-- > 1
10    

Then
$$x < 0$$
no execute
the solution of our inequality is:
$$x > 0$$

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