Let's tackle the given inequality step by step:
### Analysis of the Inequality
The given compound inequality is:
[tex]\[ -9 \leq 31 \leq 18 \][/tex]
Here, we need to determine if there exists any value that satisfies both parts of the inequality simultaneously.
Step 1: Analyze the first part of the inequality.
[tex]\[ -9 \leq 31 \][/tex]
This is a true statement because [tex]\(-9\)[/tex] is less than [tex]\(31\)[/tex].
Step 2: Analyze the second part of the inequality.
[tex]\[ 31 \leq 18 \][/tex]
This is a false statement because [tex]\(31\)[/tex] is greater than [tex]\(18\)[/tex].
Since both parts of the inequality must be true for the inequality to hold true, and here one part is false, the combined inequality is invalid.
### Graphing the Solution Set
Given that the combined inequality does not hold true, there is no value [tex]\(x\)[/tex] that satisfies [tex]\( -9 \leq 31 \leq 18 \)[/tex]. Therefore, the solution set is empty.
On a number line, this would be represented by no shading or markings, as there are no valid values.
### Representing the Solution Set in Interval Notation
Since the inequality is invalid and there is no value that satisfies [tex]\( -9 \leq 31 \leq 18 \)[/tex]:
- The solution set is an empty set.
The interval notation for an empty set is:
[tex]\[ \emptyset \][/tex]
or
[tex]\[ () \][/tex]
### Summary
Part 1: The graph of the solution set is blank, indicating no values satisfy the inequality.
Part 2: The solution set in interval notation is:
[tex]\[ \emptyset \][/tex]
or
[tex]\[ () \][/tex]
