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:

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

In order to solve the inequality:

$−p+4<−9$

Subtract both sides of the inequality by 4, as

$$\begin{gathered} −p+4<−9 \\ −p+4−4<−9−4 \\ −p<−13 \\ p>13 \end{gathered}$$

Thus, the inequality is true for p strictly greater than 13, thus the solution of given inequality in interval form is, as $\left(13,\mathrm{∞}\right)$.

Now, to check the answer solution for the given inequality first check the solution at end point by converting it into an equation. Putting pequals to13in the left hand side as

$$\begin{gathered} −13+4=−9 \\ =\text{RightHandside} \end{gathered}$$

Now put any value any value of pgreater than13, say20and check whether it satisfies the inequality, as

$$\begin{gathered} −p+4<−9 \\ −20+4<−9 \\ −16<−9\left[\text{True}\right] \end{gathered}$$

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