9x-4(x-7)≤0 inequation

Given the inequality:
$$9 x - 4 \left(x - 7\right) \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$9 x - 4 \left(x - 7\right) = 0$$
Solve:
Given the linear equation:

9*x-4*(x-7) = 0

Expand brackets in the left part

9*x-4*x+4*7 = 0

Looking for similar summands in the left part:

28 + 5*x = 0

Move free summands (without x)
from left part to right part, we given:
$$5 x = -28$$
Divide both parts of the equation by 5

x = -28 / (5)

$$x_{1} = - \frac{28}{5}$$
$$x_{1} = - \frac{28}{5}$$
This roots
$$x_{1} = - \frac{28}{5}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{28}{5} + - \frac{1}{10}$$
=
$$- \frac{57}{10}$$
substitute to the expression
$$9 x - 4 \left(x - 7\right) \leq 0$$
$$\frac{\left(-57\right) 9}{10} - 4 \left(-7 + - \frac{57}{10}\right) \leq 0$$

-1/2 <= 0

the solution of our inequality is:
$$x \leq - \frac{28}{5}$$

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