5-3(a-2)<5 inequation

Given the inequality:
$$5 - 3 \left(a - 2\right) < 5$$
To solve this inequality, we must first solve the corresponding equation:
$$5 - 3 \left(a - 2\right) = 5$$
Solve:
Given the linear equation:

5-3*(a-2) = 5

Expand brackets in the left part

5-3*a+3*2 = 5

Looking for similar summands in the left part:

11 - 3*a = 5

Move free summands (without a)
from left part to right part, we given:
$$- 3 a = -6$$
Divide both parts of the equation by -3

a = -6 / (-3)

$$a_{1} = 2$$
$$a_{1} = 2$$
This roots
$$a_{1} = 2$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$a_{0} < a_{1}$$
For example, let's take the point
$$a_{0} = a_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 2$$
=
$$\frac{19}{10}$$
substitute to the expression
$$5 - 3 \left(a - 2\right) < 5$$
$$5 - 3 \left(-2 + \frac{19}{10}\right) < 5$$

53    
-- < 5
10    

but

53    
-- > 5
10    

Then
$$a < 2$$
no execute
the solution of our inequality is:
$$a > 2$$

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