Given six consecutive integers with a sum of seven times the second number, write an algebraic equation for this situation.

x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 = 7(x + 1)

Step-by-step explanation:

Equations

The situation can be written as an algebraic equation by setting the variables as follows:

x = first integer

x + 1 = second integer

x + 2 = third integer

x + 3 = fourth integer

x + 4 = fifth integer

x + 5 = sixth (and last) integer

The sum of all six numbers must be equal to 7 times the second number, thus:

x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 = 7(x + 1)

because they could drop even lower..