Let x, a, δ ∈ R with δ > 0. Show that the following two statements are equivalent. (a) |x − a| < δ
(b) a − δ < x < a + δ
Hint: Distinguish between the cases x − a ≥ 0 and x − a < 0.

What is the percent of increase for a population that changed from 438,000 to 561,000

Brian, chris, and damien took a math test that had 20 questions. the number of questions brian got right is 14 more than the number of questions chris got right. damien correctly answered 2 less than the number of questions chris answered correctly. if brian and damien have the same score, which statement is true?

Trent wants to buy 2 packs of trading cards for 3 dollars each. the trading card packs that trent normally buys tend to come in packs of 6, 10, 12, or 15 cards. after selecting 2 packs, trent found that the first pack of cards cost 25 cents per card, and the second pack cost 30 cents per card. trent uses this information to write the equations below in order to compare c, the number of cards in each pack.