I dont understand how to distributive property to rewrite the equation n than solve for each variable ?

Hey Jeannette, to distribute something to is when you have a coefficient in front of something in parenthesis and you need to multiply all of those numbers in the parenthesis by the coefficient.

Example:

3(X + 2Y) → 3X + 6Y

You can also do this in reverse, pulling out the common factor.

6X + 3Y → 3(2X + Y)

With the problem we have here there are two ways we can do it.

We can pull out the 3, leaving a fraction.

3K - 7 → 3(K - 7/3)

We can pull out the 3, leaving a fraction.

3K - 7 → 3(K - 7/3)

Or, to keep it at whole numbers we can subtract 32 from each side, and then factor

3K - 7 = 32 → 3K - 39 = 0 → 3(K - 13) = 0

If you are trying to solve the equation, then you just need to get K by itself on one side. This is similar to what we did before. Add 7 to both sides, and then divide each side by 3.

3K - 7 = 32 → 3K = 39 → K = 13