x≥18,5. inequation

Given the inequality:
$$x \geq \frac{37}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$x = \frac{37}{2}$$
Solve:
Given the linear equation:

x = (37/2)

Expand brackets in the right part

x = 37/2

$$x_{1} = \frac{37}{2}$$
$$x_{1} = \frac{37}{2}$$
This roots
$$x_{1} = \frac{37}{2}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{37}{2}$$
=
$$\frac{92}{5}$$
substitute to the expression
$$x \geq \frac{37}{2}$$
$$\frac{92}{5} \geq \frac{37}{2}$$

92/5 >= 37/2

but

92/5 < 37/2

Then
$$x \leq \frac{37}{2}$$
no execute
the solution of our inequality is:
$$x \geq \frac{37}{2}$$

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