To solve the inequality \(5x + 3 > 8x + 9\), follow these steps:

### Step 1: Subtract \(5x\) from both sides to move all terms involving \(x\) to one side.
\[
5x + 3 - 5x > 8x + 9 - 5x
\]
This simplifies to:
\[
3 > 3x + 9
\]

### Step 2: Subtract 9 from both sides to move the constant terms to one side.
\[
3 - 9 > 3x + 9 - 9
\]
This simplifies to:
\[
-6 > 3x
\]

### Step 3: Divide both sides by 3 to solve for \(x\).
\[
\frac{-6}{3} > \frac{3x}{3}
\]
This simplifies to:
\[
-2 > x
\]

### Final solution:
\[
x < -2
\]

So the solution to the inequality is \(x < -2\).

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the solution change if the inequality was \(5x + 3 < 8x + 9\)?
2. What happens if the inequality involves a negative coefficient in front of \(x\)?
3. Can you graph the solution \(x < -2\) on a number line?
4. How would you check if the solution is correct by substituting values for \(x\)?
5. What are the properties of inequalities when multiplying or dividing by negative numbers?

**Tip:** When dividing or multiplying both sides of an inequality by a negative number, remember to flip the inequality sign!

Learn how to solve the inequality 5x + 3 > 8x + 9 with a step-by-step guide. This solution demonstrates the process of manipulating inequalities and the properties of inequalities, suitable for students in Grades 7-9.

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