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)

4a. is 3 miles every hour

4b. is 1/3 of an hour per mile

step-by-step explanation:

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation: