Find two consecutive even integers such that their sum is equal to the difference of three times larger and two times the smaller.

Question

I need help right away, I also need step by step.

Answer 1

"two consecutive even integers" Let's use x and x+2 [note: even]

"their sum" is expressed as (x) + (x+2)

"is equal to" that's "="

"difference of" "three times larger" and "two times the smaller" this is 3(x+1) - 2x

The equation: (x) + (x+2) = 3(x+2) - 2x

Now, find x:

x + x + 2 = 3(x+2) - 2x

2x + 2 = 3x + 6 - 2x

2x + 2 = x + 6

x = 4

and (x+2) = 6

CHECK (very important)

Is 4 + 6 = 3*(6) - 2*(4) ??

10 = 18 - 8 ??

10 = 10 ? yes.

Answer 2

Consecutive even integers are always two apart from each other.

For example:

2, 4

16, 18

100, 102

Therefore, if we call the smaller of the two x, then the larger would be x + 2.

Their sum is equal to the difference of 3 times the larger and two times the smaller

This can be thought as the equation:

x + (x+2) = 3(x+2) - 2(x)

On the left of the equation, we have their sum and on the right of the equation we have the difference of 3 times the larger and 2 times the smaller

Now all you have to do is solve for x and x+2