Given the inequality:
$$5 - 4 x > 3$$
To solve this inequality, we must first solve the corresponding equation:
$$5 - 4 x = 3$$
Solve:
Given the linear equation:
-4*x+5 = 3
Move free summands (without x)
from left part to right part, we given:
$$- 4 x = -2$$
Divide both parts of the equation by -4
x = -2 / (-4)
$$x_{1} = \frac{1}{2}$$
$$x_{1} = \frac{1}{2}$$
This roots
$$x_{1} = \frac{1}{2}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{1}{2}$$
=
$$\frac{2}{5}$$
substitute to the expression
$$5 - 4 x > 3$$
$$5 - \frac{2 \cdot 4}{5} > 3$$
17/5 > 3
the solution of our inequality is:
$$x < \frac{1}{2}$$
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