91Ó°ÊÓ

To graph the endpoint with strict inequality < or >, use the open parenthesis or a hollow circle at that endpoint.

To graph the endpoint with inequality symbol $≤\text{or}â‰\yen$, use the bracket or a solid circle at that endpoint.

Properties of inequality:

$$\begin{gathered} 1.b≤c⇒bÂ\pm a≤cÂ\pm a \\ 2.b≤c⇒ab≤ac,\text{if}a>0 \\ 3.b≤c⇒abâ‰\yen ac,\text{if}a<0 \end{gathered}$$

In order to solve the inequality:

$\frac{1}{3}y≤5$

Multiply both sides by 3, as

$$\begin{gathered} \frac{1}{3}y≤5 \\ \frac{1}{3}y×3≤5×3 \\ y≤15 \end{gathered}$$

Thus, the inequality is true for y less than equal to 15, thus the solution of given inequality in interval form is, as $\left(−\mathrm{∞},15\right]$.

Now, to check the answer solution for the given inequality first check the solution at end point by converting it into an equation. Putting y equals to 15 in left hand side

$$\begin{gathered} \frac{15}{3}=5 \\ =\text{RightHandside} \end{gathered}$$

Now put any value any value of y less than 15, say 12 and check whether it satisfies the inequality, as

$\frac{12}{3}=4<5$

Since, both conditions are satisfied thus solution of inequality is correct.