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:

$12≤t−9$

Add 9 both sides of the inequality, as

$$\begin{gathered} 12≤t−9 \\ 12+9≤t−9+9 \\ 21≤t \end{gathered}$$

Thus, the solution of the given inequality is every number greater than or equals to 21, this can be represented in the interval form, as $\left[21,\mathrm{∞}\right)$.

Now, in order to sketch the graph of the solution of the inequality, since the interval of solution at left end point 21 is not strict, so use a solid circle at point 21. And the solution interval at right endpoint $\mathrm{∞}$, thus every point greater than 21 is in the solution interval of given inequality. The graph of the solution of inequality is shown below: