Cant figure out what to do (equations)
1)Find three consecutive even integers with a sum of -30
2)Find four consecutive integers with a sum of 26
n-2, n, n+2
n-2 + n + n+2 = -30
3 n = -30
n=-10
so
-12 , -10, -8
=======================
n + n+1 + n+2 + n+3 = 26 etc
I get it but why do we do n-2?
The second one equals to 32
I did n-2 to get n in the middle so I would get a simple 3n on the left. I could just as well have used:
n + n+2 + n+4
or
n-4 + n-2 + n
Also notice that the fact that it is odd or even is not used. Luckily it comes out with n even.
To solve these equations, we can use algebraic expressions. Let's break down each problem step by step.
1) Find three consecutive even integers with a sum of -30:
Let's assume the first even integer is x. Since the integers are consecutive, the second even integer will be x + 2, and the third even integer will be x + 4.
The sum of these three integers can be represented as: x + (x + 2) + (x + 4) = -30
Now, we can solve this equation to find the value of x:
3x + 6 = -30
3x = -30 - 6
3x = -36
x = -36 / 3
x = -12
So the first even integer (x) is -12. The second even integer will be -12 + 2 = -10, and the third even integer will be -12 + 4 = -8.
Therefore, the three consecutive even integers with a sum of -30 are -12, -10, and -8.
2) Find four consecutive integers with a sum of 26:
Let's assume the first integer is x. Since the integers are consecutive, the second integer will be x + 1, the third integer will be x + 2, and the fourth integer will be x + 3.
The sum of these four integers can be represented as: x + (x + 1) + (x + 2) + (x + 3) = 26
Now, we can solve this equation to find the value of x:
4x + 6 = 26
4x = 26 - 6
4x = 20
x = 20 / 4
x = 5
So the first integer (x) is 5. The second integer will be 5 + 1 = 6, the third integer will be 5 + 2 = 7, and the fourth integer will be 5 + 3 = 8.
Therefore, the four consecutive integers with a sum of 26 are 5, 6, 7, and 8.