https://file.aiquickdraw.com/mathbot/file/1725914980811ev9rjdxo.jpg

Let's solve the inequality provided in the image:

The inequality is:

\[
-6x + 9 > 7x + 74
\]

### Step 1: Move all terms involving \(x\) to one side.
We can start by subtracting \(7x\) from both sides:

\[
-6x - 7x + 9 > 74
\]
\[
-13x + 9 > 74
\]

### Step 2: Isolate the constant.
Now, subtract 9 from both sides:

\[
-13x > 74 - 9
\]
\[
-13x > 65
\]

### Step 3: Solve for \(x\).
Next, divide both sides by \(-13\), remembering to flip the inequality sign because we are dividing by a negative number:

\[
x < \frac{65}{-13}
\]
\[
x < -5
\]

### Conclusion:
The solution set is \(x < -5\), which corresponds to option **b. x < -5**.

---

Would you like more details or have any questions about this?

Here are some related questions:
1. How do you solve an inequality when there is a negative coefficient?
2. Why does dividing by a negative flip the inequality sign?
3. What is the difference between solving inequalities and equations?
4. Can inequalities have multiple solution sets?
5. How do you graph an inequality on a number line?

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

What is the solution set for the inequality -6x + 9 > 7x + 74?

Find the solution set for the inequality -6x + 9 > 7x + 74 with a step-by-step explanation. Learn how to manipulate linear equations and apply the properties of inequalities. Suitable for students in Grades 7-9.

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