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:

$p−4<−7$

Add 4 both sides of the inequality, as

$$\begin{gathered} p−4<−7 \\ p−4+4<−7+4 \\ p<−3 \end{gathered}$$

Thus, the solution of the given inequality is every number is strictly less than $-3$, this can be represented in the interval form, as width="69">−∞,−3.

Now, in order to sketch the graph of the solution of the inequality, since the interval of solution at left end point $-3$is strict, so use a hollow circle at point $-3$. And the solution interval at left endpoint $−\mathrm{∞}$, thus every point strictly less than $-3$is in the solution interval of given inequality. The graph of the solution of inequality is shown below: