Chapter 4, Problem 1CRE

To determine

The graph inequality which suits the given description and express the set in interval notation

Answer to Problem 1CRE

Solution:

The interval notation for the inequality is $\left[5,12\right]$ .

Explanation of Solution

Given:

The statement “All real numbers at least $5$ , but not more than $12$ ”

The word “at least $5$ ” means all numbers equal or greater than $5$ .

The word “not more than $12$ ” means all numbers that are equal or less than $12$ .

We are looking for all real numbers which are greater than or equal to $5$ and less than or equal to $12$ . Let $x$

represent the numbers satisfying the above condition. This can be represented in different way given below:

Condition: “All real numbers at least $5$ , but not more than $12$ ”

Inequality: $5\le x\le 12$

Graph: Closed circle represent the number is included & Open circle indicates number not included.

Interval notation: The interval notation for the inequality $5\le x\le 12$ is $\left[5,12\right]$ .

Conclusion:

The graph for the given inequality is

And the interval notation is $\left[5,12\right]$ .