Solve the inequality. Graph and check your solutions.
4/3 <=n + 3
Which of the following is the graph of the solution set?
To solve the inequality, we can start by subtracting 3 from both sides:
4/3 - 3 <= n
Combining like terms gives us:
-5 2/3 <= n
To graph the solution set, we can plot a closed circle on -5 2/3 on a number line and shade to the right:
<===[-5 2/3===>
Finally, we can check our solution by choosing a value to the right of -5 2/3, such as -5. Plugging -5 into the original inequality gives us:
4/3 <= -5 + 3
4/3 <= -2
Since this is not true, we can conclude that the graph of the solution set is:
===>[-5 2/3===]
To solve the inequality and graph the solution set, we will follow these steps:
Step 1: Subtract 3 from both sides of the inequality:
4/3 - 3 <= n
Simplifying the left side:
- 9/3 <= n
Step 2: Simplify the inequality:
-3 <= n
Step 3: Graph the solution set on a number line:
To graph the solution set -3 <= n, we need to plot all values of n that satisfy this inequality. It means that all values of n that are greater than or equal to -3 will be included in the solution set.
______________o___________
Step 4: Check the solution set:
To check the solution set, substitute any value greater than or equal to -3 into the original inequality and see if it holds true.
For example, let's check n = -3:
4/3 <= -3 + 3
4/3 <= 0
0 is the equal sign, so it's true.
Similarly, if we check n = 0:
4/3 <= 0 + 3
4/3 <= 3
3 is greater than 4/3, so it's also true.
Since the inequality holds true for these values, we can conclude that the solution set graph is a closed dot at -3 on a number line, to the right, including all values greater than -3.
To solve the inequality 4/3 <= n + 3, we need to isolate n on one side of the inequality.
First, subtract 3 from both sides of the inequality:
4/3 - 3 <= n + 3 - 3
-5/3 <= n
Now, let's graph the solution set.
To represent the solution set on a number line, we start by drawing a number line and marking a point on it. This point will represent n.
Next, we mark all the numbers less than or equal to -5/3. Since -5/3 is a negative number, we mark the numbers to the left of -5/3 on the number line.
Finally, we shade the region to the left of -5/3 on the number line to represent the solution set.
So, the graph of the solution set is:
<-----------------[=========]
To check the solution, we can choose a value of n from the shaded region and substitute it back into the original inequality to see if it holds true. For example, if we choose n = -2, we can substitute it into the inequality and check:
4/3 <= -2 + 3
4/3 <= 1
Since 4/3 is indeed less than or equal to 1, the solution n = -2 is correct.
Therefore, the correct graph of the solution set is:
<-----------------[=========]