91Ó°ÊÓ

Properties of inequalities are written in following table:

To simplify given inequality, first simplify parentheses then use properties of inequalities. Add same numbers from both sides does not change the sign of inequality. Finally use division property, divide both sides by same negative number reverse the sign of inequality as shown below

$\begin{array}{c}12\left(\frac{1}{4}−\frac{n}{3}\right)≤−6n\\ 3−4n≤−6n\\ 3−4n+4n≤−6n+4n\\ 3≤−2n\\ \frac{3}{−2}â‰\yen \frac{−2n}{−2}\\ −\frac{3}{2}â‰\yen n\end{array}$

The solution set of the inequality contains all real numbers less than or equal to $-\frac{3}{2}$

As, $-\frac{3}{2}$ is included in the set so bracket is used with it also $-∞$ is not included so parentheses is used with it.

In interval form solution set is $\left(-∞,-\frac{3}{2}\right]$

Assolution set of the inequality is all real numbers less than or equal to $-\frac{3}{2}$

So arrow is towards $-∞$ and dot on $-\frac{3}{2}$ shows it is included in the solution set.