Solve the inequality. Graph and check your solutions.
y-7>-16
To solve the inequality, we will isolate the variable "y" on one side of the inequality sign.
First, we will add 7 to both sides of the inequality:
y - 7 + 7 > -16 + 7
Simplifying, we have:
y > -9
To graph the solution on a number line, we plot an open circle at -9 and shade the region to the right, as the inequality is "greater than."
-9|
|
------|---------------->
|_________________
Next, we can check the solution. For example, if we substitute y = -8 into the original inequality:
(-8) - 7 > -16
-15 > -16
This is true, so the solution is confirmed. All values greater than -9 will satisfy the inequality.
To solve the inequality y - 7 > -16, we will follow these steps:
Step 1: Add 7 to both sides of the inequality to isolate the variable y:
y - 7 + 7 > -16 + 7
This simplifies to:
y > -9
Step 2: Graph the solution on a number line. Since y is greater than -9, we will place an open circle on -9 and draw an arrow to the right, indicating that the solution includes all values greater than -9.
```
-9 |
|
=>---->|
```
Step 3: Check the solution by substituting a test value. Let's choose y = -8:
y - 7 > -16
(-8) - 7 > -16
-15 > -16
Since -15 is greater than -16, the solution is valid.
Therefore, the graph of the inequality y - 7 > -16 is as shown above, and the solution includes all values greater than -9.
To solve the inequality y - 7 > -16, you need to isolate y on one side of the inequality sign.
Step 1: Add 7 to both sides of the inequality:
y - 7 + 7 > -16 + 7
y > -9
Now we have solved the inequality. The solution is y > -9.
To graph the solution, you need to draw a number line and mark the value -9 with an open circle (∅) to indicate that it is not included in the solution. Then, draw an arrow extending to the right to represent all values of y greater than -9.
--------∅--->
-9
Lastly, to check the solutions, you can pick any value greater than -9, plug it into the original inequality, and check if it holds true. For example, let's check y = 0:
0 - 7 > -16
-7 > -16
Since -7 is greater than -16, the inequality holds true. Therefore, any value greater than -9 will satisfy the inequality.