x+2*x-3>0 inequation

Given the inequality:
$$\left(x + 2 x\right) - 3 > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(x + 2 x\right) - 3 = 0$$
Solve:
Given the linear equation:

x+2*x-3 = 0

Looking for similar summands in the left part:

-3 + 3*x = 0

Move free summands (without x)
from left part to right part, we given:
$$3 x = 3$$
Divide both parts of the equation by 3

x = 3 / (3)

$$x_{1} = 1$$
$$x_{1} = 1$$
This roots
$$x_{1} = 1$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 1$$
=
$$\frac{9}{10}$$
substitute to the expression
$$\left(x + 2 x\right) - 3 > 0$$
$$-3 + \left(\frac{9}{10} + \frac{2 \cdot 9}{10}\right) > 0$$

-3/10 > 0

Then
$$x < 1$$
no execute
the solution of our inequality is:
$$x > 1$$

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