HELP me now plz

Question

Alex has 395 cards. Michael has 250 cards. They both give the same number of cards to their friend Austin. After giving cards to Austin, the numbers of cards Alex has is less than two times the amount of cards Michael has. Write and solve an inequality to determine the range of cards they gave Austin. (Write your answer in a complete sentence.)

Answer 1

Ah... our favorite... a bit of algebra!

Alex has 395 cards

AL = 395

Michael has 250 cards

MI = 250

They both give the same number of cards to their friend Austin

AU = 2x and AL = 395-x and MI = 250-x

After giving cards to Austin, the numbers of cards Alex has is less than two times the amount of cards Michael has

AL < 2 x MI or 395 - x < 2 (250 - x)

=> 395 - x < 500 - 2x

=> x < 105

now check boundaries:

At 105: AU = 210, AL = 290, MI = 145, 2MI = 290 and 290 = 290 (excluded, equal)

At 104: AU = 208, AL = 291, MI = 146, 2MI = 292 and 291 < 292

At 1: AU = 2, AL = 394, MI = 249, 2MI = 498 and 394 < 498

At 0: AU = 0, AL = 395, MI = 250, 2MI = 500 and 395 < 500 (exluded because they "gave cards")

At -10: AU = -20, AL = 405, MI = 260, 2MI = 520 and 405 < 520 (excluded because can't "give" minus cards)

I think it's reasonable, based on the phrasing of the question, to exclude giving 0 or -ve number of cards to Austin. Even though this meets inequality x < 105.

Alex can give between 1 and 104 cards, inclusive, to Austin. Between Alex and Michael, Austin can get between 2 and 208 cards, inclusive.