Question

express the interval in set - builder notation and graph the interval on a number line (-∞, - 6)
select the correct choice below and, if necessary, fill out the answer box to complete your choice
a. the solution set in set - builder notation is {x | }
(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.
a. number line graph with a closed - circle at - 6 and arrow pointing left
b. number line graph with an open - circle at - 6 and arrow pointing left
c. number line graph with arrow pointing left and right
d. number line graph with an open - circle at - 6 and arrow pointing right

Explanation:

Step1: Recall set - builder notation

The interval \((-\infty,-6)\) represents all real numbers \(x\) such that \(x < - 6\). In set - builder notation, it is written as \(\{x|x < - 6\}\).

Step2: Recall number - line graphing

For the interval \((-\infty,-6)\), we use an open - circle at \(-6\) (because \(-6\) is not included in the interval) and draw an arrow to the left to represent all numbers less than \(-6\).

Answer:

A. The solution set in set - builder notation is \(\{x|x < - 6\}\)
B. The correct graph is B.