The sum of seven consecutive integers is 7x. What is the value of the largest integer in terms of x?

Question

I don’t understand how to solve this problem. Can someone please explain it to me?

Answer 1

Let x = the smallest integer.  A consecutive integer is 1 larger than the previous integer, hence seven consecutive integers are:

 

x, (x+1), (x+2), (x+3), (x+4), (x+5), (x+6)

 

Each integer is one larger than the integer before it.  For example, if x = 3, then the 7 consecutive integers would be 3, 4, 5, 6, 7, 8, 9, 10.  The largest integer in terms of x is the last one, (x+6).

Answer 2

you have to write the equation as follows...

(x-3)+(x-2)+(x-1)+x+(x+1)+(x+2)+(x+3)=7x

simplify to get...

7x-6+6=7x

7x=7x

the value of the largest integer in terms of x is (x+3)

example: let x=9

6+7+8+9+10+11+12=7*9

63=63 and x+3=9+3=12