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Solve and graph the solution to each of the inequslities

The image shows the inequality \( x + 3 \leq 2 \). Let's solve this inequality and then graph the solution.

### Solution:
1. Start with the inequality:
   \[
   x + 3 \leq 2
   \]
2. Subtract 3 from both sides to isolate \( x \):
   \[
   x \leq 2 - 3
   \]
   \[
   x \leq -1
   \]

So, the solution to the inequality is \( x \leq -1 \).

### Graphing the solution:
- The graph of this inequality consists of all values of \( x \) that are less than or equal to \( -1 \).
- On a number line:
  - Draw a solid dot at \( x = -1 \) to represent that \( -1 \) is included in the solution.
  - Shade all values to the left of \( -1 \) (indicating \( x < -1 \)).

Would you like me to graph this on a number line, or would you like more details on any step?

Here are 5 related questions for practice:
1. How would the solution change if the inequality was \( x + 3 < 2 \)?
2. What happens if you multiply both sides of an inequality by a negative number?
3. How do you solve the inequality \( 2x - 5 \geq 3 \)?
4. What is the graphical difference between \( x \leq -1 \) and \( x < -1 \)?
5. Can inequalities have multiple solutions, and how would you graph such cases?

**Tip**: When solving inequalities, always reverse the inequality sign if you multiply or divide by a negative number.

Solve and graph the solution to the inequality x + 3 ≤ 2.

Learn how to solve the inequality x + 3 ≤ 2 and graph the solution on a number line. This problem covers key algebra concepts and properties of inequalities. Suitable for students in Grades 6-8.

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