Chapter 5, Problem 4MCQ

To determine

To solve the inequality:

$12\le t-9$

And to graph the solution on a number line.

Answer to Problem 4MCQ

  $\left[21,\infty \right)$

Explanation of Solution

Given:

$12\le t-9$

Concept Used:

• To graph the endpoint with strict inequality $<\text{ or}>$, use the open parenthesis or a hollow circle at that endpoint.
• To graph the endpoint with inequality symbol $\le \text{ or}\ge$ , use the bracket or a solid circle at that endpoint.
• Properties of inequality:

1.$b\le c\Rightarrow b\pm a\le c\pm a$

2.$b\le c\Rightarrow ab\le ac,\text{ if }a>0$

3.$b\le c\Rightarrow ab\ge ac,\text{ if }a<0$

Calculation:

In order to solve the inequality

$12\le t-9$

Add 9 both sides of the inequality, as

  $\begin{array}{c}12\le t-9\\ \Rightarrow 12+9\le t-9+9\\ \Rightarrow 21\le t-0\\ \Rightarrow 21\le t\end{array}$

Thus, the solution of given inequality is every number greater than and equals to 21, this can be represented in interval form, as

  $\left[21,\infty \right)$

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 $\infty$ , thus every point greater than 21 is in the solution interval of given inequality. The graph of the solution of inequality is shown below: