Question

express the interval in set - builder notation and graph the interval on a number line. (-6,6 select the correct choice below and, if necessary, fill in the answer box to complete your choice. the solution set in set - builder notation is {x|-6 < x ≤ 6} (type an inequality or a compound inequality.) a. the solution set is all real numbers. b. c. d. there is no solution. choose the correct graph below.

Explanation:

Step1: Analyze the interval (-6,6]

The interval (-6,6] in set - builder notation is $\{x|-6 < x\leqslant6\}$. On a number - line, we use an open circle at - 6 (because - 6 is not included in the set) and a closed circle at 6 (because 6 is included in the set), and we draw a line segment connecting them.

Step2: Check the graphs

Option A has an open circle at - 6 and a closed circle at 6 with the line segment in between, which represents the interval (-6,6].

Answer:

A. (The graph with an open circle at - 6, a closed circle at 6, and a line segment connecting them)