Question

The sum of two consecutive integers is −67. Find the integers.

Answer 1

let's take a peek at some consecutive integers

2, 3, 4, 5, 6, 7......

notice, to get a consecutive from any of those, we simply hop back or forth one number, 5±1 gives us the consecutive ones of 4 and 6.

so let's say our first integer is "a", then our next one is "a + 1", and we know they sum up to -67.

`\bf (a)+(a+1)=-67\implies 2a=-68\implies a=\cfrac{-68}{2}\implies \boxed{a=-34} \\\\\\ \stackrel{\textit{and consecutive one is}}{a+1\implies -33}`