4x>-17 inequation

Given the inequality:
$$4 x > -17$$
To solve this inequality, we must first solve the corresponding equation:
$$4 x = -17$$
Solve:
Given the linear equation:

4*x = -17

Divide both parts of the equation by 4

x = -17 / (4)

$$x_{1} = - \frac{17}{4}$$
$$x_{1} = - \frac{17}{4}$$
This roots
$$x_{1} = - \frac{17}{4}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{17}{4} + - \frac{1}{10}$$
=
$$- \frac{87}{20}$$
substitute to the expression
$$4 x > -17$$
$$\frac{\left(-87\right) 4}{20} > -17$$

-87/5 > -17

Then
$$x < - \frac{17}{4}$$
no execute
the solution of our inequality is:
$$x > - \frac{17}{4}$$

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