https://file.aiquickdraw.com/mathbot/file/1725433454954aefuupqs.jpg

Please only solve questions 5, 8, and 9 please.

Let's solve the requested problems: questions 5, 8, and 9.

### Question 5:
**Write the inequality indicated by this graphic.**

Since you provided a photo, the graphic for this question shows a number line with a shaded region that likely indicates an inequality. To accurately solve this, I would need to know the exact numbers or points marked on the number line and whether the shaded region is open or closed at the endpoints.

If you can describe the graphic in more detail, I'll be able to provide the correct inequality. Otherwise, the typical answer would be something like \(a \leq x < b\) or \(a < x \leq b\), depending on the number line's details.

### Question 8:
**Find the area.**

The diagram shows a right triangle with legs labeled \(15\) and \(8\). To find the area of a right triangle, you use the formula:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

Here, the base is \(15\) and the height is \(8\):

\[
\text{Area} = \frac{1}{2} \times 15 \times 8 = \frac{1}{2} \times 120 = 60
\]

So, the area of the triangle is **60 square units**.

### Question 9:
**Expand and reduce each resulting term:**

Given: \(\frac{6a}{x} - \frac{12a}{x}\)

First, expand and simplify the expression inside the fraction:

\[
\frac{6a - 12a}{x} = \frac{-6a}{x}
\]

The expression simplifies to \(-\frac{6a}{x}\).

So, the simplified form is \(-\frac{6a}{x}\).

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Would you like further details on any of these solutions, or do you have any questions? Here are five related questions that might interest you:

1. How would you solve a similar inequality if the endpoints on the number line were reversed?
2. What happens to the area of a triangle if both the base and height are doubled?
3. How do you determine if a region on a number line represents an inclusive or exclusive inequality?
4. How would the expression in Question 9 change if the denominator were different?
5. Can you calculate the perimeter of the triangle given in Question 8?

**Tip:** When working with inequalities, always pay attention to whether the inequality includes the endpoint (closed circle) or not (open circle) on a number line.

This page covers solutions for three mathematical problems involving inequalities, calculating the area of a right triangle, and simplifying algebraic expressions. Suitable for students in Grades 8-10, it includes key concepts and step-by-step solutions.

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