91Ó°ÊÓ

Properties of inequalities are written in following table:

To simplify given inequality, use division property of inequalities. Divide same positive number from both sides does not change inequality as shown below

$\begin{array}{c}5â‰\yen 3x\\ \frac{5}{3}â‰\yen \frac{3x}{3}\\ \frac{5}{3}â‰\yen x\end{array}$

The solution set of the inequality $\frac{5}{3}â‰\yen x$ contains $\frac{5}{3}$ greater than or equal to all real number.

In interval notation, solution set contains all real number between $-∞$ to $\frac{5}{3}$

As $-∞$ is not an end points so parentheses is used with it whereas $\frac{5}{3}$ is included in solution set so bracket is used with it.

Solution set is $\left(-∞,\frac{5}{3}\right]$

Assolution set of the inequality $\frac{5}{3}â‰\yen x$ contains $\frac{5}{3}$ greater than or equal to all real number.

So arrow is towards $-∞$ and dot on $\frac{5}{3}$ denotes it is included in the solution set.