Certainly! Let's solve and graph the inequality step-by-step:
### Step 1: Isolate the Variable
The given inequality is:
[tex]\[ n + 2 \leq 6 \][/tex]
To isolate [tex]\( n \)[/tex], we need to subtract 2 from both sides of the inequality:
[tex]\[ n + 2 - 2 \leq 6 - 2 \][/tex]
[tex]\[ n \leq 4 \][/tex]
### Step 2: Interpret the Solution
The inequality [tex]\( n \leq 4 \)[/tex] means that [tex]\( n \)[/tex] can be any number that is less than or equal to 4.
### Step 3: Graph the Inequality
To graph the inequality [tex]\( n \leq 4 \)[/tex]:
1. Draw a number line.
2. Identify the key point: Place a point at [tex]\( n = 4 \)[/tex]. Because the inequality is "less than or equal to," we will use a closed dot (●) at [tex]\( n = 4 \)[/tex] to indicate that 4 is included in the solution.
3. Shade the region: Shade the number line to the left of 4 to show that all numbers to the left of 4, including 4 itself, are solutions.
### Putting it All Together
The graph on the number line will look like this:
[tex]\[ \ldots \, \cdot \, \cdot \, \cdot \, \cdot \, \cdot \, \filledcircled{4} \longleftarrow \][/tex]
This graph represents all real numbers [tex]\( n \)[/tex] such that [tex]\( n \leq 4 \)[/tex]. The closed dot at 4 indicates that 4 is included in the solution set, and the arrow extending to the left shows all numbers less than 4 are also part of the solution.
In conclusion, you would choose the graph that has a closed circle at 4 and shading to the left, representing all numbers [tex]\( n \)[/tex] that satisfy the inequality [tex]\( n \leq 4 \)[/tex].
