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 5, as

$$\begin{gathered} 4<\frac{c}{5} \\ 4×5<\frac{c}{5}×5 \\ 20<c \\ c>20 \end{gathered}$$

Thus, the inequality is true for c greater than 20, thus the solution of given inequality in interval form is, as $\left(20,\mathrm{∞}\right)$.

Now, to check the answer solution for the given inequality first check the solution at end point by converting it into an equation. Putting c equals to 20 in right hand side

$$\begin{gathered} \frac{20}{5}=4 \\ =\text{LeftHandside} \end{gathered}$$

Now put any value any value of c greater than 20, say 30 and check whether it satisfies the inequality, as

$$\begin{gathered} 4<\frac{c}{5} \\ 4<\frac{30}{5} \\ 4<6\left[\text{True}\right] \end{gathered}$$

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