(1/2)x+35->8 inequation

Given the inequality:
$$\frac{x}{2} + 35 > 8$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{x}{2} + 35 = 8$$
Solve:
Given the linear equation:

(1/2)*x+35 = 8

Expand brackets in the left part

1/2x+35 = 8

Move free summands (without x)
from left part to right part, we given:
$$\frac{x}{2} = -27$$
Divide both parts of the equation by 1/2

x = -27 / (1/2)

$$x_{1} = -54$$
$$x_{1} = -54$$
This roots
$$x_{1} = -54$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-54 + - \frac{1}{10}$$
=
$$- \frac{541}{10}$$
substitute to the expression
$$\frac{x}{2} + 35 > 8$$
$$\frac{-541}{2 \cdot 10} + 35 > 8$$

159    
--- > 8
 20    

Then
$$x < -54$$
no execute
the solution of our inequality is:
$$x > -54$$

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