Chapter P.1, Problem 14E

Solution

The inequality for the interval of real numbers represented by the given graph.

The inequality for the given interval of real numbers is: $-2\le x<2$

Given:

The graph of inequality:

  

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:

The given set of real numbers represents the real numbers that are greater than or equal to $-2$ and less than 2.

Since there is a close bracket at the left endpoint, use the inequality sign $\le$ with $-2$ . Also note that there is an open parenthesis at the right endpoint, so use the strict inequality symbol $<$ with 2.

Therefore, the inequality for the given interval of real numbers is $-2\le x<2$ .