Question

express the interval in set - builder notation and graph the interval on a number line.
$(-2,\infty)$
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set in set - builder notation is $\\{x|x > - 2\\}$
(use integers or fractions for any numbers in the expression.)
b. the solution set is all real numbers.
c. there is no solution.
choose the correct answer below.

Explanation:

Step1: Understand interval notation

The interval \((-2,\infty)\) means all real numbers \(x\) such that \(x > - 2\). In set - builder notation, this is written as \(\{x|x > - 2\}\).

Step2: Analyze number - line graph

For the number - line graph of \(x>-2\), we have an open circle at \(x = - 2\) (because \(-2\) is not included in the interval) and an arrow pointing to the right (towards positive infinity).

Answer:

A. The solution set in set - builder notation is \(\{x|x > - 2\}\) and the correct number - line graph is the one with an open circle at \(-2\) and an arrow to the right (assuming option A in the number - line choices has this characteristic).