Solve the inequality. Graph and check your solutions.

Question

3/2 <= n + 2
n >= - 1/2 (Type an integer or a simplified fraction.) Which of the following is the graph of the solution set?

Answer 1

The given inequality is 3/2 <= n + 2.

To solve the inequality, we will subtract 2 from both sides to isolate n:

3/2 - 2 <= n + 2 - 2
-1/2 <= n

So the solution to the inequality is n >= -1/2.

To graph the solution set, we will draw a number line and shade the region to the right of -1/2:

<=========]----->
-2 -1/2 0

The graph will have a closed circle at -1/2 and an arrow pointing to the right.

Lastly, we need to check our solution. Let's substitute n = -1/2 into the original inequality:

3/2 <= -1/2 + 2
3/2 <= 3/2

The inequality is true when n = -1/2, so our solution is correct.

Therefore, the correct graph for the solution set is option C.