let us say first(lesser) even integer is x
so that our next(greater) consecutive integer will be x+2
Framing expressions from given information:
the lesser of two consecutive even integers is five more than half the greater
half the greater here means (x+2) / 2
framing equation:
[tex] x= \frac{x+2}{2} +5 [/tex]
subtracting (x+2)/2 from left side, to bring common terms together:
[tex] x-\frac{x+2}{2} =5 [/tex]
finding lcd
lcd of 2 and 1 is 1, so converting both denominators into lcd ,
[tex] \frac{2x}{2} - \frac{x+2}{2} = 5 [/tex]
[tex] \frac{2x-x-2}{2} =5 [/tex]
[tex] \frac{x-2}{2} =5 [/tex]
cross multiplying
[tex] x-2=10 [/tex]
taking -2 on right and adding
[tex] x=10+2 [/tex]
Answer x=12 and x+2=14
So lesser even integer is 12 and greater is 14
