https://file.aiquickdraw.com/mathbot/file/1727970903808ya3y03eo.jpg

The inequality given in the image is:

\[
5x + 3 > 9x + 8
\]

Let's solve this step by step:

### Step 1: Move all terms involving \(x\) to one side of the inequality.
Subtract \(9x\) from both sides:

\[
5x - 9x + 3 > 8
\]

This simplifies to:

\[
-4x + 3 > 8
\]

### Step 2: Move the constant terms to the other side.
Subtract 3 from both sides:

\[
-4x > 8 - 3
\]

\[
-4x > 5
\]

### Step 3: Solve for \(x\).
To solve for \(x\), divide both sides by \(-4\). **Remember, when dividing by a negative number, the inequality sign reverses**:

\[
x < \frac{5}{-4}
\]

\[
x < -\frac{5}{4}
\]

So, the solution to the inequality is:

\[
x < -\frac{5}{4}
\]

Would you like further details on solving inequalities? 

### Related questions:
1. How do you solve inequalities with variables on both sides?
2. What happens when you divide an inequality by a negative number?
3. Can you graph the solution to this inequality on a number line?
4. What is the difference between strict and non-strict inequalities?
5. How do you handle inequalities with fractions?

**Tip**: Always remember to flip the inequality when multiplying or dividing both sides by a negative number!

Learn how to solve the inequality 5x + 3 > 9x + 8 with a detailed step-by-step solution. This algebra problem covers solving inequalities by simplifying and applying the property of reversing the inequality sign when dividing by a negative number. Suitable for students in Grades 7-9.

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