Question

Find the coordinates of the vertices of the figures formed by y -< x + 2, x + 2 -< 6, and y >- -2
A)(0,0),(2,4),(8,-2)
B)(-4,-2),(2,4),(8,-2)
C)(-4,-2),(4,2),(8,-2)
D)(-2,-4),(2,4),(8,-2)
I chose B

this one confused me this is all the work to show:
-2 -< -4 + 2
2 + 4 -< 6
-2

Answer 1

the way u did it, if I try to do the others, Aren't they all true though?

Answer 2

No, all are not true

Answer 3

We have this:

(y -< x + 2) = point 1.

(x + 2 -< 6) = point 2.

(y >- -2) = point 3.

Replace all inequality symbols with an equal sign for easy simplification.

Point 3:

y >- -2 becomes y = -2

We just found y.

We plug y = -2 in point 1 to find x.

-2 = x + 2

-2 - 2 = x

-4 = x

We know that y = -2 and x = -4.

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Notice that the next point to follow in choice B is (2,4), where x = 2 and y = 4.

We plug that into all three points to see if we get a true statement.

(y -< x + 2) = point 1.

4 -< 2 + 2...true statement

(x + 2 -< 6) = point 2.

2 + 4 -< 6...true statement

(y >- -2) = point 3.

4 >- -2...true statement

So far, it appears that choice B is correct.

===================================

What is the next point given in choice B? It is point (8, -2).

We do the same-->plug to check for true statement.

(y -< x + 2) = point 1.

-2 -< 8 + 2...true statement

(x + 2 -< 6) = point 2.

8 + 2 -< 6...false statement

(y >- -2) = point 3.

-2 >- -2...true statement

We know that choice A and D cannot be the answers. We just found out that choice B is most likely not the answer because of the false statement.

I would say the answer is choice C.