←minus 5---minus 4----minus 3-------minus 2--------minus 1-----------0--------------------------------1→
So for the two equations: Not sure how hard you want them but....
15+1=16 and 13+ 18=21
For the open equation.
2x + x(5+7)=105
Greetings and Happy Holidays! Let x represent the smaller, even integer.
Let (x+2) represent the larger, even integer.
We can create an
algebraic equation to solve for the numbers:
Simplify:
![x=\frac{1}{2}x+1+2](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B2%7Dx%2B1%2B2)
Add ![\frac{-1}{2}x](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B2%7Dx)
to both sides:
![(x)+(\frac{-1}{2}x)=(\frac{1}{2}x+3)+(\frac{-1}{2}x)](https://tex.z-dn.net/?f=%28x%29%2B%28%5Cfrac%7B-1%7D%7B2%7Dx%29%3D%28%5Cfrac%7B1%7D%7B2%7Dx%2B3%29%2B%28%5Cfrac%7B-1%7D%7B2%7Dx%29)
Divide both sides by
![\frac{1}{2}x](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dx)
![\frac{\frac{1}{2}x}{ \frac{1}{2}}=\frac{3}{\frac{1}{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7Dx%7D%7B%20%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Cfrac%7B3%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D%20)
![x=\frac{3}{1}(2)](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B3%7D%7B1%7D%282%29)
The Answer Is:
![\boxed{x=6}](https://tex.z-dn.net/?f=%5Cboxed%7Bx%3D6%7D)
and
![x+2=6](https://tex.z-dn.net/?f=x%2B2%3D6)
![\boxed{x=8}](https://tex.z-dn.net/?f=%5Cboxed%7Bx%3D8%7D)
The two consecutive even integers are
6 and 8.
I hope this helped!
-Benjamin
(x-4)(x+9) is equivalent to x^2+5x-36
all you need to do is factor the equation