Question

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

Answer 1

`-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`