The sum of three consecutive integers is - 96. What is the larger integer

Let the first integer be x. Since the three integers are consecutive, the next two integers will be x + 1 and x + 2, respectively. Collectively the integers add to equal - 96. That means you can set our expressions for the integers to - 96, like so:

-96 = x + (x + 1) + (x + 2)

Now we can solve algebraically for x.

-96 = x + (x + 1) + (x + 2)

-96 = x + x + 1 + x + 2

-96 = 3x + 3

-99 = 3x

-33 = x

The first integer is x, so the first integer is - 33.

The second integer is x + 1, so the second integer is - 32.

The third integer is x + 2, so the third integer is - 31.

Let's quickly add these integers to see if their sum is - 96.

-33 + (-32) + (-31)

-33 - 32 - 31 = - 96

These three consecutive integers add to equal - 96. The question asks for the larger integer. Recall that the higher the number in front of a negative sign, the smaller the number. - 2 is smaller than - 1. That means the order of the integers from largest to smallest is - 31, - 32, - 33.

Answer:

The largest integer is - 31.