0,9x<5,4 inequation

Given the inequality:
$$\frac{9 x}{10} < \frac{27}{5}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{9 x}{10} = \frac{27}{5}$$
Solve:
Given the linear equation:

(9/10)*x = (27/5)

Expand brackets in the left part

9/10x = (27/5)

Expand brackets in the right part

9/10x = 27/5

Divide both parts of the equation by 9/10

x = 27/5 / (9/10)

$$x_{1} = 6$$
$$x_{1} = 6$$
This roots
$$x_{1} = 6$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 6$$
=
$$\frac{59}{10}$$
substitute to the expression
$$\frac{9 x}{10} < \frac{27}{5}$$
$$\frac{9 \cdot 59}{10 \cdot 10} < \frac{27}{5}$$

531       
--- < 27/5
100       

the solution of our inequality is:
$$x < 6$$

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