Question

How do you find three consecutive integers whose sum is -33?

Answer 1

See the entire solution process below:

Explanation:

Let's call the first integer `i`. Because they are consecutive integers by definition we can add `1` to get the next integer and `2` to get the third integer. Therefore are three consecutive integers are: `i`, `i + 1` and `i + 2`.

Because the three integers sun to or add up to `-33` we can write:

`i + i + 1 + i + 2 = -33`

We can now solve for `i` as follows:

`3i + 3 = -33`

`3i + 3 - color(red)(3) = -33 - color(red)(3)`

`3i + 0 = -36`

`3i = -36`

`(3i)/color(red)(3) = -36/color(red)(3)`

`(color(red)(cancel(color(black)(3)))i)/cancel(color(red)(3)) = -12`

`i = -12`

The first integer is `-12`

The second integer is `i + 1` or `-12 + 1 = -11`

The third integer is `i + 2` or `-12 + 2 = -10`

The three consecutive integers whose sum is -33 are -12, -11 and -10.