1/1-2x>0 inequation

Given the inequality:
$$1 - 2 x > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$1 - 2 x = 0$$
Solve:
Given the linear equation:

1/1-2*x = 0

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

x = -1 / (-2)

$$x_{1} = \frac{1}{2}$$
$$x_{1} = \frac{1}{2}$$
This roots
$$x_{1} = \frac{1}{2}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{1}{2}$$
=
$$\frac{2}{5}$$
substitute to the expression
$$1 - 2 x > 0$$
$$1 - \frac{2 \cdot 2}{5} > 0$$

1/5 > 0

the solution of our inequality is:
$$x < \frac{1}{2}$$

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