The  sum  of three consecutive integers is  three more  than  twice the middle integer. create an equation and solve to find the integers. can someone me out? and explain and show work!

Our numbers are 2, 3, and 4.

To begin to answer this question, we must first find out what the number are (as variables). Since they are consecutive, and there are three of them, the number are x, (x + 1), and (x + 2).

Now we need to see what information the question is giving us, and set up the equation. The first part says the sum of the three consecutive numbers, so we need to add the three consecutive numbers. That is x + (x + 1) + (x + 2). Now we continue. Since we know that the middle number is (x + 1), twice the middle number is 2(x + 1), and twice the middle number plus 3 is 2(x + 1) + 3. Now we can set up our equation.

x + (x + 1) + (x + 2) = 2(x + 1) + 3

Now we solve

3x + 3 = 2x + 5

x = 2

That means that our numbers are 2, 3, and 4.