Solve the inequality. Graph and check your solutions.
y - 5 > - 19
y > - 14 (Simplify your answer.) Which of the following is the graph of the solution?
The graph of the solution is a number line with a closed circle at -14 and an arrow pointing to the right.
To solve the inequality, we'll isolate the variable y.
Given inequality: y - 5 > -19
Add 5 to both sides of the inequality:
y - 5 + 5 > -19 + 5
y > -14
So the solution to the inequality is y > -14.
To graph the solution, we'll draw a number line and mark -14 on it. We will then shade the region to the right of -14, because y is greater than -14.
The graph of the solution would look like this:
```
----------------------------
| -14
----------------------------
```
To check the solutions, you can pick any value greater than -14 and substitute it into the inequality. For example, let's substitute y = -10 (greater than -14) into the original inequality:
-10 - 5 > -19
-15 > -19
Since -15 is indeed greater than -19, we can conclude that the solution y > -14 is correct.
To solve the inequality and graph the solution, we need to follow these steps:
Step 1: Solve the inequality:
Start by adding 5 to both sides of the inequality:
y - 5 + 5 > -19 + 5
y > -14
Step 2: Graph the solution:
To graph the solution, we need to draw a number line and mark the point -14 on it. Since the inequality is y > -14, the graph will be a shaded region to the right of -14, excluding the point itself because the inequality is strict.
Step 3: Check the solution:
To check our solution, we can substitute different values greater than -14 into the original inequality to see if they satisfy it. For example, let's try y = -10:
-10 - 5 > -19
-15 > -19
Since -15 is greater than -19, the inequality is true. We can repeat this process with different values greater than -14 to further confirm that they satisfy the inequality.
Based on the steps above, the graph of the solution is a shaded region to the right of -14 on the number line.