The sum of two consecutive integers is −13. What are the numbers?

1 Answer
Tony B
May 5, 2016

#-7-6=-13#

Explanation:

#color(blue)("There are other ways of solving this but I have opted to demonstrate a")#
#color(blue)("method that can be used for other condition. For example:")##color(blue)("The sum of 3 consecutive odd numbers and the next even number is 71")#

#color(brown)(" 15, 17, 19 and 20" -> (n)+(n+2)+(n+4)+(n+5)=71)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let the first number be #n#
Let the second number be #n+1#

Then #" "n+n+1=-13#

#2n+1=-13#

Subtract 1 from both sides

#2n=-13-1=-14#

Divide both sides by 2

#2/2xxn=-14/2#

But #2/2=1#

#n=-7#

So the second number is #" "-7+1=-6#

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