(3/10)x⩾9/100 inequation

Given the inequality:
$$\frac{3 x}{10} \geq \frac{9}{100}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{3 x}{10} = \frac{9}{100}$$
Solve:
Given the linear equation:

(3/10)*x = 9/100

Expand brackets in the left part

3/10x = 9/100

Divide both parts of the equation by 3/10

x = 9/100 / (3/10)

$$x_{1} = \frac{3}{10}$$
$$x_{1} = \frac{3}{10}$$
This roots
$$x_{1} = \frac{3}{10}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{3}{10}$$
=
$$\frac{1}{5}$$
substitute to the expression
$$\frac{3 x}{10} \geq \frac{9}{100}$$
$$\frac{3}{5 \cdot 10} \geq \frac{9}{100}$$

3/50 >= 9/100

but

3/50 < 9/100

Then
$$x \leq \frac{3}{10}$$
no execute
the solution of our inequality is:
$$x \geq \frac{3}{10}$$

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