(1/5)*(x*2+3x-10)>1 inequation

Given the inequality:
$$\frac{\left(2 x + 3 x\right) - 10}{5} > 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\left(2 x + 3 x\right) - 10}{5} = 1$$
Solve:
Given the linear equation:

(1/5)*(x*2+3*x-10) = 1

Expand brackets in the left part

1/5x*2+3*x-10 = 1

Looking for similar summands in the left part:

-2 + x = 1

Move free summands (without x)
from left part to right part, we given:
$$x = 3$$
$$x_{1} = 3$$
$$x_{1} = 3$$
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:
$$x_{0} < x_{1}$$
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
$$\frac{\left(2 x + 3 x\right) - 10}{5} > 1$$
$$\frac{-10 + \left(\frac{2 \cdot 29}{10} + \frac{3 \cdot 29}{10}\right)}{5} > 1$$

9/10 > 1

Then
$$x < 3$$
no execute
the solution of our inequality is:
$$x > 3$$

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