Question

express the interval as an inequality and graph the interval on a number line.
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set in interval notation is (type an inequality or a compound inequality.)
b. the solution set is all real numbers.
c. there is no solution.
choose the correct graph below

Explanation:

Step1: Analyze the interval notation

The interval \((-\infty,-7)\) represents all real numbers \(x\) such that \(x < - 7\).

Step2: Check the options for the solution set

• Option A: If we write it as an inequality, it is \(x < - 7\).
• Option B: The set of all real numbers would be \((-\infty,\infty)\), which is not the case here.
• Option C: There is a solution set (all numbers less than \(-7\)), so this is incorrect.

Step3: Check the graph

• Option A's graph (if it has an open - circle at \(-7\) and a line extending to the left) is the correct graph for \(x < - 7\). The open - circle at \(-7\) indicates that \(-7\) is not included in the set (since the interval is \((-\infty,-7)\) and not \([-\infty,-7]\)).

Answer:

A. The solution set in set - builder notation is \(\{x|x < - 7\}\) and the correct graph is the one with an open - circle at \(-7\) and a line extending to the left (assuming Option A's graph is of this form).