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The inequality you provided is:

\[
-\frac{3}{2}x - \frac{3}{5}y > x - y - 2
\]

To graph this inequality, let's first transform it into a more convenient form.

### Step-by-step transformation:

1. Move all terms involving \(x\) and \(y\) to the left side:
   \[
   -\frac{3}{2}x - \frac{3}{5}y - x + y > -2
   \]
   
2. Combine like terms for \(x\) and \(y\):
   \[
   \left(-\frac{3}{2} - 1\right)x + \left(-\frac{3}{5} + 1\right)y > -2
   \]
   
   Simplifying the coefficients:
   \[
   -\frac{5}{2}x + \frac{2}{5}y > -2
   \]

3. Multiply through by 10 (to eliminate the fractions):
   \[
   -25x + 4y > -20
   \]

4. Solve for \(y\) in terms of \(x\):
   \[
   4y > 25x - 20
   \]
   \[
   y > \frac{25}{4}x - 5
   \]

Now, you can graph the line \(y = \frac{25}{4}x - 5\), and the inequality \(y > \frac{25}{4}x - 5\) will represent the area above the line.

### Graph:

- The slope of the line is \( \frac{25}{4} \), meaning the line is steeply inclined.
- The y-intercept is \(-5\).
- You will shade the region above the line because the inequality is \( y > \frac{25}{4}x - 5 \).

Would you like me to generate a graph for this inequality?

### Relative questions:
1. How would the graph change if the inequality was \( y < \frac{25}{4}x - 5 \)?
2. What is the significance of the slope and y-intercept in this equation?
3. How do you graph inequalities with both \(x\) and \(y\) terms on a coordinate plane?
4. What are the methods for checking which side of the line to shade when graphing inequalities?
5. How do we interpret the solution region for systems of inequalities?

**Tip:** When graphing inequalities, always remember to use a dashed line for ">" or "<" inequalities, as the boundary is not included in the solution.

Explore how to graph the inequality -3/2x - 3/5y > x - y - 2 step-by-step. Learn about combining like terms, transforming equations, and graphing the resulting inequality. Perfect for students in Grades 9-10 studying algebra and linear inequalities.

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