(16)x≥(16)3 inequation

Given the inequality:
$$16 x \geq 48$$
To solve this inequality, we must first solve the corresponding equation:
$$16 x = 48$$
Solve:
Given the linear equation:

(16)*x = (16)*3

Expand brackets in the left part

16x = (16)*3

Expand brackets in the right part

16x = 16*3

Divide both parts of the equation by 16

x = 48 / (16)

$$x_{1} = 3$$
$$x_{1} = 3$$
This roots
$$x_{1} = 3$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 3$$
=
$$\frac{29}{10}$$
substitute to the expression
$$16 x \geq 48$$
$$\frac{16 \cdot 29}{10} \geq 48$$

232/5 >= 48

but

232/5 < 48

Then
$$x \leq 3$$
no execute
the solution of our inequality is:
$$x \geq 3$$

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