4x-160x+1<0 inequation

Given the inequality:
$$\left(- 160 x + 4 x\right) + 1 < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(- 160 x + 4 x\right) + 1 = 0$$
Solve:
Given the linear equation:

4*x-160*x+1 = 0

Looking for similar summands in the left part:

1 - 156*x = 0

Move free summands (without x)
from left part to right part, we given:
$$- 156 x = -1$$
Divide both parts of the equation by -156

x = -1 / (-156)

$$x_{1} = \frac{1}{156}$$
$$x_{1} = \frac{1}{156}$$
This roots
$$x_{1} = \frac{1}{156}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{1}{156}$$
=
$$- \frac{73}{780}$$
substitute to the expression
$$\left(- 160 x + 4 x\right) + 1 < 0$$
$$1 + \left(\frac{\left(-73\right) 4}{780} - \frac{\left(-73\right) 160}{780}\right) < 0$$

78/5 < 0

but

78/5 > 0

Then
$$x < \frac{1}{156}$$
no execute
the solution of our inequality is:
$$x > \frac{1}{156}$$

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