Question

Can someone help me I don't get this???
Select ALL of the following inqualities that have an infinite number of integer solutions
F: x<2 and x>4
G: 2≤x≤4
H: x≤2 or x≤4
J: x≥2 and x≥4

Answer 1

Look at the first inequality. Is there an integer that can be at the same time less than 2 and greater than 4?

Answer 2

no, that would be impossible so would that answer be a no solution?

Answer 3

No, not yet. That means there are no solutions at all to choice F, so get rid of choice F.

Answer 4

got it

Answer 5

Now let's look at choice G: x needs to be an integer that is greater than or equal to 2 and less than or equal to 4. Can you name all integers this is true of?

Answer 6

2,3,4

Answer 7

Excellent. That is not an infinite number of intergers. It's just 3 of them, so get rid of choice G.

Answer 8

right!

Answer 9

Now in choice H, you are missing a number. Can you correct it?

Answer 10

oh sorry! x≤2

Answer 11

Ok. Let's look at choice H. You need an integer less than or equal to 2 or an integer less than or equal to 4. Either choice will be good. How many integers less than or equal to 2 are there? How many integeres less than or equal to 4 are there?

Answer 12

there would be a lot if you had included negatives, and for 4 the same

Answer 13

Correct. Since the set of integers includes all positive whole numbers, all negative whole numbers and zero, there is an infinite number of them. Therefore, keep choice H.

Answer 14

that makes sense!

Answer 15

Now let's look at our final choice, choice J. It's similar to choice H, only greater than instead of less than. How many integers aree there that are greater than or equal to 2 _and_ greater than or equal to 4?

Answer 16

oh I see that is similar, a lot right?

Answer 17

Correct. The answer is all integers greater than or equal to 4. That is still an infinite set. So keep choice J also. Final answer is: H and J

Answer 18

thank u so much! ☺

Answer 19

You're a good student! Great working with you. You're welcome.