49-25x<0 inequation

Given the inequality:
$$- 25 x + 49 < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$- 25 x + 49 = 0$$
Solve:
Given the linear equation:

49-25*x = 0

Move free summands (without x)
from left part to right part, we given:
$$- 25 x = -49$$
Divide both parts of the equation by -25

x = -49 / (-25)

$$x_{1} = \frac{49}{25}$$
$$x_{1} = \frac{49}{25}$$
This roots
$$x_{1} = \frac{49}{25}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{49}{25}$$
=
$$\frac{93}{50}$$
substitute to the expression
$$- 25 x + 49 < 0$$
$$- \frac{25 \cdot 93}{50} + 49 < 0$$

5/2 < 0

but

5/2 > 0

Then
$$x < \frac{49}{25}$$
no execute
the solution of our inequality is:
$$x > \frac{49}{25}$$

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