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

Answer 1

#-7-6=-13#

#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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Answer 2

Abigail Allen

Let ( x ) represent the smaller integer. Then, the next consecutive integer would be ( x + 1 ). Since their sum is -13, we can set up the equation:

[ x + (x + 1) = -13 ]

Solving for ( x ):

[ 2x + 1 = -13 ] [ 2x = -14 ] [ x = -7 ]

So, the two consecutive integers are -7 and -6.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.