SOLUTION: if a, b, and c are three consecutive positive integers, which of the following is true? A. a + c < 2b B. a + b < c C. a + c > 2b D. b + c > a I think the answer is D.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: if a, b, and c are three consecutive positive integers, which of the following is true? A. a + c < 2b B. a + b < c C. a + c > 2b D. b + c > a I think the answer is D.       Log On


   

Question 837600: if a, b, and c are three consecutive positive integers, which of the following is true? A. a + c < 2b B. a + b < c C. a + c > 2b D. b + c > a I think the answer is D.
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
As in all consecutive integer problems, start with:

a = n
b = n+1
c = n+2

Let's substitute in each one:

A.   a + c < 2b
   n + n+2 < 2(n+1)
    2n + 2 < 2n + 2

That's false, because they are equal, so = holds, not <

B.   a + b < c
   n + n+1 < n+2
      2n+1 < n+2
         n < 1

That's false because there are no positive integers less than 1.

C.   a + c > 2b
   n + n+2 > 2(n+1)
      2n+2 > 2n+2 

That's false, because they are equal, so = holds, not >

D.     b + c > a
   n+1 + n+2 > n
        2n+3 > n
           n > -3

That's true. Any positive integer is greater than any negative integer.
So you're right.  But to do the above is the way to show your work.

Edwin