Solve and graph the solution to each of the inequality$$  $$$$ x+1 $$≠$$ -2 $$

To solve the inequality 

\[
x + 1 \neq -2,
\]

we need to isolate $ x $.

### Step 1: Solve the inequality

1. Start by subtracting $ 1 $ from both sides:

   \[
   x + 1 - 1 \neq -2 - 1.
   \]

2. Simplify:

   \[
   x \neq -3.
   \]

### Step 2: Graph the solution

Since the inequality $ x \neq -3 $ indicates that $ x $ can take any value except $-3$, we represent this on a number line.

- Draw a number line.
- Mark the point $ -3 $ with an open circle (indicating that $-3$ is not included in the solution set).
- Shade all other parts of the number line.

Here's how it should look:

1. The number line extends indefinitely in both directions.
2. An open circle is placed at $ x = -3 $.
3. All other numbers are included in the solution.

Would you like me to generate a graph of this solution? 

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**Related Questions:**

1. How do you graph a solution on a number line?
2. What does it mean when a solution has an open circle?
3. How do you solve inequalities involving more complex expressions?
4. How can inequalities change when squared or cubed?
5. What are common mistakes when solving inequalities?

**Tip:** Always use an open circle on a number line to indicate values that are not included in the solution set, especially with "not equal to" inequalities.

Solve and graph the solution to the inequality x + 1 ≠ -2

Learn how to solve and graph the inequality x + 1 ≠ -2 step by step. This lesson explains the algebraic manipulation and graphing techniques on a number line, focusing on the properties of inequalities. Suitable for Grades 6-8.

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