(3*x/4)-x>2 inequation

Given the inequality:
$$- x + \frac{3 x}{4} > 2$$
To solve this inequality, we must first solve the corresponding equation:
$$- x + \frac{3 x}{4} = 2$$
Solve:
Given the linear equation:

(3*x/4)-x = 2

Expand brackets in the left part

3*x/4-x = 2

Looking for similar summands in the left part:

-x/4 = 2

Divide both parts of the equation by -1/4

x = 2 / (-1/4)

$$x_{1} = -8$$
$$x_{1} = -8$$
This roots
$$x_{1} = -8$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-8 + - \frac{1}{10}$$
=
$$- \frac{81}{10}$$
substitute to the expression
$$- x + \frac{3 x}{4} > 2$$
$$\frac{\left(- \frac{81}{10}\right) 3}{4} - - \frac{81}{10} > 2$$

81    
-- > 2
40    

the solution of our inequality is:
$$x < -8$$

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