https://file.aiquickdraw.com/mathbot/file/1726769392878jtknx8y2.jpg

Let's solve the given compound inequalities one by one.

### First Inequality
\[
\frac{2}{3}x \leq 4
\]

To isolate \( x \), multiply both sides by \( \frac{3}{2} \):
\[
x \leq 4 \times \frac{3}{2}
\]
\[
x \leq 6
\]

### Second Inequality
\[
\frac{x}{-2} \leq -5
\]

Multiply both sides by \(-2\). Remember, multiplying by a negative number reverses the inequality sign:
\[
x \geq (-5) \times (-2)
\]
\[
x \geq 10
\]

### Compound Solution
We now have:
\[
x \leq 6 \quad \text{and} \quad x \geq 10
\]

There is no possible value for \( x \) that can satisfy both conditions simultaneously because \( x \) cannot be both less than or equal to 6 and greater than or equal to 10 at the same time. Thus, the solution is:

**No Solution**

The correct graphical representation should show that there is no overlap or solution that satisfies both inequalities, which would be option A.

### Summary:
- **Solution:** No Solution
- **Graphical Representation:** A (two separate ranges)

Would you like any further details or have any questions? Here are 5 related questions you might be interested in:

1. How do you solve compound inequalities with different directions?
2. What happens when two inequalities have no overlapping solutions?
3. How do you graph inequalities on a number line?
4. What are the steps to solve a single inequality involving fractions?
5. How does multiplying or dividing by a negative number affect an inequality?

**Tip:** Always check for overlapping regions when solving compound inequalities to determine if a solution exists.

Given the following compound inequalities, answer the questions below: 2/3x ≤ 4 and x/-2 ≤ -5. Solve the inequality, and write the solutions in the boxes below. Determine if this is possible, if it is not, select 'No Solution' below. Select the correct graphical representation of the solutions to the inequality.

Learn how to solve compound inequalities with a detailed step-by-step approach. This problem involves solving the inequalities 2/3x ≤ 4 and x/-2 ≤ -5, determining the possible solutions, and interpreting the graphical representation. Ideal for students in Grades 7-9.

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