sqrt(14-4*x)>0 inequation

Given the inequality:
$$\sqrt{14 - 4 x} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\sqrt{14 - 4 x} = 0$$
Solve:
Given the equation
$$\sqrt{14 - 4 x} = 0$$
so
$$14 - 4 x = 0$$
Move free summands (without x)
from left part to right part, we given:
$$- 4 x = -14$$
Divide both parts of the equation by -4

x = -14 / (-4)

We get the answer: x = 7/2
$$x_{1} = \frac{7}{2}$$
$$x_{1} = \frac{7}{2}$$
This roots
$$x_{1} = \frac{7}{2}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{7}{2}$$
=
$$\frac{17}{5}$$
substitute to the expression
$$\sqrt{14 - 4 x} > 0$$
$$\sqrt{14 - \frac{4 \cdot 17}{5}} > 0$$

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the solution of our inequality is:
$$x < \frac{7}{2}$$

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