Question

An airline requires carry-on luggage to weigh at most 40 pounds. Your suitcase currently weighs 10 pounds. How many pounds p are available for you to fill your suitcase with other items? I KNOW THERE ARE 30 LEFT OVER POUNDS I just have no clue how to write the inequality
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p - 10 ≤ 40; p ≤ 50
40 - p < 10; p < 30*** [think it is this one]
p + 10 ≥ 40; p ≥ 30
10 + p ≤ 40; p ≤ 30

Answer 1

You said there are 30 pounds left over and the question tells you p are the available pounds left to fill your suitcase.

So p = 30. You know this.
40 - 30 = 10 which is not less than 10, so we can discount the one you thought it was.
If the inequality said 40 - 30 <= 10 , fine - we couldn't, but it doesn't.

Now, let's look the bottom inequality.
10 + p <= 40 ... Well this is true 10 + 30 = 40 which is less than or equal to 40.
p <= 30 is also true, since p is equal to 30.

Answer 2

You seem to be having trouble with the less than and less than or equal to symbols.
Say these aloud and you should be on track to success with questions like these.

Answer 3

Note: the third inequality is actually true too, and you should find this if you have understood what I have said

Answer 4

So is it the third or fourth(bottom) inequality?
I understood what you said in the first message, also. @dc104

Answer 5

It is both.