Given the inequality:
$$3 x \leq 24$$
To solve this inequality, we must first solve the corresponding equation:
$$3 x = 24$$
Solve:
Given the linear equation:
3*x = 24
Divide both parts of the equation by 3
x = 24 / (3)
$$x_{1} = 8$$
$$x_{1} = 8$$
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:
$$x_{0} \leq x_{1}$$
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
$$3 x \leq 24$$
$$\frac{3 \cdot 79}{10} \leq 24$$
237
--- <= 24
10
the solution of our inequality is:
$$x \leq 8$$
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