If 0 < a < b < c, which of the following statements…
We are given that 0 < a < b < c and need to determine which statements are true. Let’s analyze each Roman numeral. I. 2a > b + c
2a cannot be greater than the sum of b and c. Since a + a = 2a, a < b, and a < c, a + a < b + c, or 2a < b + c. Statement I is FALSE. II. c – a > b – a
We can simplify the inequality to c > b. Since we are given that c is greater than b in the stem, c – a is greater than b – a. Statement II is TRUE.
III. c/a < b/a
We can multiply both sides by a and we have c < b (note: we don’t need to switch the inequality sign because a is positive). However, we are given that c is greater than b, so c/a can’t be less than b/a. Statement III is FALSE.
Thus, only Roman numeral II is true.