Chapter P.1, Problem 33E

Solution

The inequality and interval notation for to describe the set of numbers defined as, “Bill is at least 29 years old”.

The inequality notation is: $x\ge 29$

The interval notation is: $\left[29,\infty \right)$

Here x is the age of Bill in years.

Given:

The statement, “Bill is at least 29 years old”.

Concept Used:

• If there is the strict inequality symbol $<\text{ or}>$ , then use a parenthesis $\left(\right)$ on the interval
• If there is the inequality symbol $\le \text{ or}\ge$ , then use a bracket $\left[\right]$ on the interval
• 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.

Calculation:

Let x represents the age of Bill in years.

Since Bill is at least 29 years old, he must be 29 years or older than that, that is, x must be greater than or equal to 29.

So, the inequality notation that represents the age of Bill is $x\ge 29$ .

Since the endpoint 29 is included, use the closed bracket with 29.

Therefore, the interval notation that represent the age of Bill is $\left[29,\infty \right)$ .