Consider the two inequalities 2x - 4 < y and y < -2/3x + 2.

(b) Graph the region of the plane that satisifies either inequality, or both inequalities.

(c) Graph the region of the plane that satisifies either inequality, but NOT both.

What I don't get is that in another question, (a), not shown, it says to graph the region of the plane which satisfies both inequalities. Isn't that the same as (b)?

I also don't know how to find/do c.

Thanks!

No, not the same. Either or both is not the same as both.

c) in C, exclude the area that includes both.

To answer your first question, the region of the plane that satisfies both inequalities is indeed the same as the region of the plane that satisfies either inequality in question (b). In other words, if a point satisfies both inequalities, it satisfies either one of them individually as well.

Now let's move on to question (c) and discuss how to graph the region of the plane that satisfies either inequality, but not both.

To find the region of the plane that satisfies either inequality, but not both, we need to determine the points that satisfy either one of the inequalities individually, and then identify the points in that region that do not satisfy both.

To do this, we can follow these steps:

1. Graph the line defined by the first inequality, 2x - 4 < y:
- Rewrite the inequality in slope-intercept form: y > 2x - 4
- Plot the y-intercept at -4 on the y-axis.
- Use the slope 2/1 to find additional points.

2. Graph the line defined by the second inequality, y < (-2/3)x + 2:
- Rewrite the inequality in slope-intercept form: y < (-2/3)x + 2
- Plot the y-intercept at 2 on the y-axis.
- Use the slope -2/3 to find additional points.

3. Shade the region of the plane that satisfies either one of the inequalities individually:
- For the first inequality (y > 2x - 4), shade above the line.
- For the second inequality (y < (-2/3)x + 2), shade below the line.

4. Identify the region that satisfies either inequality, but not both:
- The region that satisfies either inequality, but not both, lies in the areas where the shading from step 3 overlaps but is not shared by both shaded regions.

By following these steps, you should be able to graph the region of the plane that satisfies either inequality, but not both.