22x+2-42x>3 inequation

Given the inequality:
$$- 42 x + \left(22 x + 2\right) > 3$$
To solve this inequality, we must first solve the corresponding equation:
$$- 42 x + \left(22 x + 2\right) = 3$$
Solve:
Given the linear equation:

22*x+2-42*x = 3

Looking for similar summands in the left part:

2 - 20*x = 3

Move free summands (without x)
from left part to right part, we given:
$$- 20 x = 1$$
Divide both parts of the equation by -20

x = 1 / (-20)

$$x_{1} = - \frac{1}{20}$$
$$x_{1} = - \frac{1}{20}$$
This roots
$$x_{1} = - \frac{1}{20}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + - \frac{1}{20}$$
=
$$- \frac{3}{20}$$
substitute to the expression
$$- 42 x + \left(22 x + 2\right) > 3$$
$$\left(\frac{\left(-3\right) 22}{20} + 2\right) - \frac{\left(-3\right) 42}{20} > 3$$

5 > 3

the solution of our inequality is:
$$x < - \frac{1}{20}$$

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