What is the algebraic expression for the sum of two consecutives even numbers
Transform each equation into standard form (on paper) and then type in the A, B, and C values.
**Remember: A must be a whole number; B and C must be integers.
Equation to Transform A (coefficient for x) B (coefficient for y) C (constant term)
y - 3 = 2(x + 1)
y = 4x - 3
1/3y = 1/2x + 2
y = 3/5(x - 1)
2y - 3x + 10 = 0
2y = -1/4x + 1
Can you help me with this please? ^
since even numbers differ by 2, you could try x and x+2
But that also works for odd numbers. (e.g., 3,5)
So, since all even numbers are multiples of 2, you should have tried
2k and 2k+2
any even number can be represented by
2n, where n ∊ N, N being the set of natural numbers.
so the next consecutive even number would be 2n+2
sum of two consecutive even numbers = 2n + 2n+2 = 4n+2
= 2(2n + 1)
nice clarification, Reiny, though I'd have said that n∊Z, the integers, since even numbers can be negative.
what, you can't make your own post?
You want Ax+By = C
So, just start shuffling things around. How hard is that?
The first order of business, if necessary, is to get rid of the fractions. So, let's do
y = 3/5(x - 1)
5y = 3(x-1)
5y = 3x-3
Almost done, you just need to get the 3x onto the left side:
-3x+5y = -3
That does fit the standard form, but I hate leading mus signs, so I'd go with
3x-5y = 3
gotten by multiplying everything by -1.
So, you try the others, and come on back if you get stuck. Not likely, I know.
To find the algebraic expression for the sum of two consecutive even numbers, we need to apply some logical thinking.
Let's assume that the first even number is represented by the variable "x". Since the numbers are consecutive, the next even number can be written as "x + 2". Adding these two numbers together gives us the sum:
x + (x + 2)
Simplifying this expression, we get:
2x + 2
Thus, the algebraic expression for the sum of two consecutive even numbers is 2x + 2.