(3x-5)^0,5<5 inequation

Given the inequality:
$$\sqrt{3 x - 5} < 5$$
To solve this inequality, we must first solve the corresponding equation:
$$\sqrt{3 x - 5} = 5$$
Solve:
Given the equation
$$\sqrt{3 x - 5} = 5$$
Because equation degree is equal to = 1/2 - does not contain even numbers in the numerator, then
the equation has single real root.
We raise the equation sides to 2-th degree:
We get:
$$\left(\sqrt{3 x - 5}\right)^{2} = 5^{2}$$
or
$$3 x - 5 = 25$$
Move free summands (without x)
from left part to right part, we given:
$$3 x = 30$$
Divide both parts of the equation by 3

x = 30 / (3)

We get the answer: x = 10

$$x_{1} = 10$$
$$x_{1} = 10$$
This roots
$$x_{1} = 10$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 10$$
=
$$\frac{99}{10}$$
substitute to the expression
$$\sqrt{3 x - 5} < 5$$
$$\sqrt{-5 + \frac{3 \cdot 99}{10}} < 5$$

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\/ 2470     
-------- < 5
   10       
    

the solution of our inequality is:
$$x < 10$$

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