Solve the inequality. Graph and check your solutions.
y - 3 > - 11
First, let's solve the inequality algebraically:
y - 3 > -11
Add 3 to both sides:
y > -8
Now, let's graph the solution:
To represent all the values of y greater than -8, we will draw an open circle at -8 on the number line and draw an arrow to the right to show that the values continue indefinitely.
Checking our solution:
Let's substitute a value greater than -8 into the original inequality to see if it holds true. For example, let's try y = 0.
0 - 3 > -11
-3 > -11
This is true, so our solution y > -8 is correct.
Graph of the solution:
y > -8
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-9 -8 -7 -6 ...
```
To solve the inequality y - 3 > -11, we can start by isolating the variable y.
First, let's add 3 to both sides of the inequality to eliminate the -3 on the left side:
y - 3 + 3 > -11 + 3
This simplifies to:
y > -8
Now that we have isolated y, we can plot this inequality on a number line. The solution includes all values of y that are greater than -8 but not equal to -8.
To graph this on a number line, draw a horizontal line and mark an open circle at -8. Then, starting from the open circle, shade the line to the right since the inequality is y > -8.
Next, let's check our solutions. We can choose a test value on either side of -8 and substitute it back into the original inequality to see if it satisfies the inequality.
For example, let's choose y = -7:
(-7) - 3 > -11
-10 > -11
This is true, so the solution y = -7 is valid.
Similarly, let's choose y = -9:
(-9) - 3 > -11
-12 > -11
This is false, so the solution y = -9 is not valid.
Therefore, the solutions to the inequality y - 3 > -11 are all values of y that are greater than -8.
To solve the inequality, we need to isolate the variable, y, on one side of the inequality sign.
Given:
y - 3 > -11
Step 1: Add 3 to both sides of the inequality:
y - 3 + 3 > -11 + 3
y > -8
So, the solution to the inequality is y > -8.
Now, let's graph the solution on a number line:
Start by drawing a number line and marking a point at -8 with an open circle.
Since the inequality is y > -8, we need to shade the number line to the right of -8 to indicate that y is greater than -8. This can be represented as a ray with an arrow pointing to the right.
Next, we need to check our solution by substituting a value on the shaded part of the number line into the original inequality to see if it holds true:
Let's choose y = 0:
0 - 3 > -11
-3 > -11
Since -3 is greater than -11, the inequality holds true for y = 0.
Therefore, the solution to the inequality y - 3 > -11 is y > -8, and it is represented by a shaded region to the right of -8 on the number line.