the sum of four consecutive integers is -72. write an equation to model this situation and find the values of the four integers

let the integers be

n, n+1, n+2, and n+3

n+n+1+n+2+n+3 = -72
4n = -78
n = - 19.5 , but n has to be an integer

Four consecutive integers CANNOT add up to -72

check:
-16-17-18-19 = -70
-17-18-19-20 = -74
-18-19-20-21 = -78

no way to get -72

To solve this problem, we need to represent the four consecutive integers using variables and write an equation based on the given information.

Let's assume that the first consecutive integer is represented by 'n'. Since we are looking for four consecutive integers, the other three integers would be 'n + 1', 'n + 2', and 'n + 3'.

To find the sum of these four consecutive integers, we can add them together:
n + (n + 1) + (n + 2) + (n + 3) = -72

Now we simplify the equation:
4n + 6 = -72

To solve for 'n', we need to isolate it. We can do this by subtracting 6 from both sides of the equation:
4n = -78

Next, we divide both sides of the equation by 4 to solve for 'n':
n = -78 / 4

Calculating this, we find that n = -19.5.

However, since we are dealing with consecutive integers, the value of 'n' should be a whole number. Therefore, -19.5 is not a valid solution.

Hence, there are no four consecutive integers whose sum is -72.