Solve the inequality. Graph and check your solutions.
y - 3 > - 11
Which of the following is the graph of the solution?
The given inequality is y - 3 > -11.
First, let's solve the inequality algebraically:
Adding 3 to both sides of the inequality, we get:
y - 3 + 3 > -11 + 3
y > -8
So, the solution to the inequality is y > -8.
To graph the solution on a number line, we draw an open circle at -8 (since y is not equal to -8) and draw an arrow to the right, indicating all values greater than -8.
The correct graph of the solution is:
<=======oo====>
To solve the inequality y - 3 > -11, we need to isolate y.
Adding 3 to both sides of the inequality, we get:
y - 3 + 3 > -11 + 3
Simplifying, we have:
y > -8
The graph of the solution would be a number line with an open circle at -8 and an arrow pointing towards the right, indicating that all values greater than -8 are solutions to the inequality.
To check the solutions, we can substitute different values greater than -8 into the inequality and see if it holds true. For example, if we substitute y = 0:
0 - 3 > -11
-3 > -11
Since -3 is indeed greater than -11, the inequality holds true. Hence, all values greater than -8 are valid solutions.
To solve the inequality, we need to isolate the variable y on one side of the inequality sign. Here's how you can do it:
1. Start with the given inequality: y - 3 > -11.
2. Add 3 to both sides of the inequality to get rid of the -3 on the left side: y - 3 + 3 > -11 + 3. This simplifies to y > -8.
So, the solution to the inequality is y > -8. Now, let's graph this solution:
To graph y > -8:
- Draw a number line and mark -8 on it.
- Since the inequality is greater than (>) -8, we need to shade the region to the right of -8 because all values greater than -8 will satisfy the inequality.
- Now, draw an open circle or an arrow on the number line to indicate that -8 itself is not included in the solution set.
The graph should look like this:
------------>
-8
Now, to check the solutions, you can pick any value greater than -8 and substitute it into the original inequality. Let's check y = 0:
0 - 3 > -11
-3 > -11 (true)
Since -3 is greater than -11, the solution y > -8 holds true.
Therefore, the correct graph of the solution is a number line with a shaded region to the right of -8, indicating y > -8.