Given the inequality:
$$12 x < 96$$
To solve this inequality, we must first solve the corresponding equation:
$$12 x = 96$$
Solve:
Given the linear equation:
12*x = 96
Divide both parts of the equation by 12
x = 96 / (12)
$$x_{1} = 8$$
$$x_{1} = 8$$
This roots
$$x_{1} = 8$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 8$$
=
$$\frac{79}{10}$$
substitute to the expression
$$12 x < 96$$
$$\frac{12 \cdot 79}{10} < 96$$
474/5 < 96
the solution of our inequality is:
$$x < 8$$
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