Categorize the following numbers as "a solution" or "not a solution" to the inequality.

4x+3>−9

To determine whether a given number is "a solution" or "not a solution" to the inequality \( 4x + 3 > -9 \), we need to check if the number satisfies the inequality.

### Step-by-step process:
1. Start with the inequality:
   \[
   4x + 3 > -9
   \]
   
2. Solve the inequality for \( x \):

   \[
   4x > -9 - 3 \quad \text{(Subtract 3 from both sides)}
   \]
   \[
   4x > -12
   \]
   \[
   x > \frac{-12}{4} \quad \text{(Divide both sides by 4)}
   \]
   \[
   x > -3
   \]

3. Conclusion: Any number greater than \(-3\) is a solution to the inequality. 

### Now, let's categorize specific numbers:
- **If \( x > -3 \), it's "a solution".**
- **If \( x \leq -3 \), it's "not a solution".**

You can provide specific numbers, and I will help you determine whether they are solutions or not.

Would you like to provide numbers to check, or shall I continue explaining further?

Here are 5 questions to expand on this:
1. What happens if you use equality instead of inequality?
2. How does the inequality change if you multiply both sides by a negative number?
3. What is the geometric interpretation of this inequality on a number line?
4. How can this inequality be applied to word problems in real-life situations?
5. What are the differences in approach between strict inequalities (\(>\)) and non-strict ones (\( \geq \))?

**Tip:** Always flip the inequality sign when multiplying or dividing both sides by a negative number.

Categorize the following numbers as 'a solution' or 'not a solution' to the inequality: 4x + 3 > −9

Learn how to solve the inequality 4x + 3 > -9 and categorize numbers as solutions or not with a step-by-step process. This problem explores key algebraic concepts related to inequalities and solution sets, perfect for students in Grades 6-8.

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