How do you find three consecutive even integers such that the sum of twice the first and the third is 2 less than three times the third integer?

1 Answer
Sep 11, 2017

The numbers are 2, 4 and 6

Explanation:

So, we want 3 consecutive even integers. We can represent them by the following notations:

#x#, #x+2# and #x+4#

Now for our equation:

  • The sum of twice the first and the third:
    #2x+2(x+4)#
  • Two less than three times the third:
    #3(x+4)-2#

Now we set those two equal to each other and solve for #x#
#2x+2(x+4)=3(x+4)-2#

#2x+2x+8=3x+12-2larr# expanding both sides

#4x+8=3x+10larr# adding the #x#'s and numbers

#4x-3x=10-8larr# subtracting both sides by #-3x# and #-8#

#x=2#

So our other two numbers are:
#x+2=4" "# and #" "x+4=6#