Given the inequality:
$$\frac{x}{2} \geq 4$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{x}{2} = 4$$
Solve:
Given the linear equation:
(1/2)*x = 4
Expand brackets in the left part
1/2x = 4
Divide both parts of the equation by 1/2
x = 4 / (1/2)
$$x_{1} = 8$$
$$x_{1} = 8$$
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:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 8$$
=
$$\frac{79}{10}$$
substitute to the expression
$$\frac{x}{2} \geq 4$$
$$\frac{79}{2 \cdot 10} \geq 4$$
79
-- >= 4
20
but
79
-- < 4
20
Then
$$x \leq 8$$
no execute
the solution of our inequality is:
$$x \geq 8$$
_____
/
-------•-------
x1