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:
[tex]x=\frac{(x+2)}{2}+2[/tex]
Simplify:
[tex]x=\frac{1}{2}x+1+2[/tex]
[tex]x=\frac{1}{2}x+3[/tex]
Add [tex]\frac{-1}{2}x[/tex] to both sides:
[tex](x)+(\frac{-1}{2}x)=(\frac{1}{2}x+3)+(\frac{-1}{2}x)[/tex]
[tex](\frac{1}{2}x)=3[/tex]
Divide both sides by [tex]\frac{1}{2}x[/tex]
[tex]\frac{\frac{1}{2}x}{ \frac{1}{2}}=\frac{3}{\frac{1}{2}} [/tex]
[tex]x=\frac{3}{1}(2)[/tex]
[tex]x=\frac{6}{1}[/tex]
The Answer Is:
[tex]\boxed{x=6}[/tex]
and
[tex]x+2=6[/tex]
[tex]\boxed{x=8}[/tex]
The two consecutive even integers are 6 and 8.
I hope this helped!
-Benjamin
