Now that we’ve learned how to solve word problems involving the sum of consecutive integers, let’s narrow it down and this time, focus on word problems that only involve finding the sum of consecutive even integers.
But before we start delving into word problems, it’s important that we have a good understanding of what even integers, as well as consecutive even integers, are.
Even Integers
We know that even numbers are integers that can be divided exactly or evenly by 22. Thus, the general form of the even integer nn, is n = 2kn=2k, where kk is also an integer.
In other words, since even numbers are the multiples of 22, we can represent an even integer nn by 2k2k, where kk is also an integer. So if we have the even integers 1010 and 1616,
Side 1 = short side = 2x-3
side 2 = longer side = (short side) + 6 = (2x-3)+6 = 2x+3
side 3 = side 2 = 2x+3
Side 2 and side 3 are the longer two congruent sides
Add up the three sides and set them equal to the given perimeter of 33. Solve for x
(side1)+(side2)+(side3) = perimeter
(2x-3)+(2x+3)+(2x+3) = 33
(2x+2x+2x) + (-3+3+3) = 33
6x+3 = 33
6x+3-3 = 33-3
6x = 30
6x/6 = 30/6
x = 5
If x = 5, then the longer sides are 2*x+3 = 2*5+3 = 10+3 = 13 inches each
(note: the short side is 2*x-3=2*5-3=10-3 = 7 inches)
Answer: 13 inches
The slope of this line is -2.
rise/run
rise = 4
run = -2
4
------- = -2
-2
Using the points (1,0) & (0,2)
2 - 0 2
----------- = ----- = -2
0 - 1 -1
The inverse of this function is y = x - 
You can find the inverse of any function by switching the x and y values and then solving for the new y value. Once you've done that, what will be left over is the inverse function.
y = 
----> Swap x and y
x = -----> Subtract 3/4 from both sides.
x - = y ----> rearrange to appropriate order
y = x -
And that is your inverse function.
A
- Harvard university professor
