Solve the inequality. Graph and check your solutions.
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?
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.
To solve the inequality 3/2 <= n + 2, we can subtract 2 from both sides to isolate the variable n:
3/2 - 2 <= n + 2 - 2
-1/2 <= n
So, the solution to the inequality is n >= -1/2.
To graph this solution on a number line, we start at -1/2 and shade everything to the right, including -1/2. Since the inequality is "greater than or equal to," we use a closed circle on -1/2 to represent that it is included in the solution set.
The graph on the number line would look like this:
---------------------------●-------->
The filled-in circle (●) represents -1/2, and the arrow pointing to the right indicates that the solution includes all values greater than -1/2.
To check the solutions, you can select any value greater than or equal to -1/2 and substitute it into the original inequality to see if it holds true. For example, let's check n = 0:
3/2 <= 0 + 2
3/2 <= 2
This inequality is indeed true because 3/2 is less than or equal to 2. Therefore, the solution n >= -1/2 is correct.
To solve the inequality 3/2 <= n + 2, we need to isolate the variable n.
Subtract 2 from both sides of the inequality:
3/2 - 2 <= n
Simplify:
-1/2 <= n
Therefore, the solution to the inequality is n >= -1/2.
To graph this solution set, we need to shade the region on the number line that satisfies the inequality. Since n is greater than or equal to -1/2, we will shade everything to the right of -1/2 on the number line.
Graphically, this would be represented by a closed circle at -1/2 and shading everything to the right.
Therefore, the correct graph of the solution set is a closed circle at -1/2 with shading to the right.
Note: To check the solution, you can choose any value greater than or equal to -1/2, substitute it into the original inequality, and verify if it holds true.