Question

Solve the inequality. Graph and check your solutions.
minus11less thanyminus5
Question content area bottom
Part 1
y
▼
less than or equals
less than
greater than or equals
greater than
  
enter your response here
​(Simplify your​ answer.)

Answer 1

To solve the inequality \(-11 < y - 5\), we can start by isolating \(y\).

1. Add \(5\) to both sides of the inequality:
\[
-11 + 5 < y
\]
This simplifies to:
\[
-6 < y
\]

2. In standard form, we can write this as:
\[
y > -6
\]

### Summary of the solution:
The solution to the inequality is \(y > -6\).

### Graphing the solution:
On a number line, you would represent \(y > -6\) with an open circle at \(-6\) (indicating that \(-6\) is not included in the solution) and shade to the right to show that all values greater than \(-6\) are included.

### Checking your solution:
You can check the solution by choosing a number greater than \(-6\) (e.g., \(0\)):
- Substitute \(0\) into the original inequality:
\[
-11 < 0 - 5
\]
\[
-11 < -5 \quad \text{(True)}
\]

Now, check a number less than \(-6\) (e.g., \(-7\)):
- Substitute \(-7\) into the original inequality:
\[
-11 < -7 - 5
\]
\[
-11 < -12 \quad \text{(False)}
\]

Thus, the solution \(y > -6\) is verified.