Question

express the interval in set - builder notation and graph the interval on a number line.
4,8
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 | 4≤x≤8} (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 from - 2 to 10, arrow on both ends
b. number line from - 2 to 10, open circles at 4 and 8, line in between
c. number line from - 2 to 10, closed circles at 4 and 8, line in between
d. number line from - 2 to 10, closed circle at 4, arrow to the right

Explanation:

Step1: Interpret interval notation

The interval $[4,8]$ uses square brackets, meaning both endpoints 4 and 8 are included. This translates to the inequality $4 \leq x \leq 8$, so set-builder notation is $\{x \mid 4 \leq x \leq 8\}$.

Step2: Match to number line graph

A closed (filled) dot at 4 and 8, with a line connecting them, represents including both endpoints. This matches option C's graph.

Answer:

For the set-builder notation: A. The solution set in set-builder notation is $\{x \mid 4 \leq x \leq 8\}$
For the graph: C. (The number line with closed brackets at 4 and 8, and a blue segment between them)