The sum of three consecutive odd integers is 14 more than three times the 2nd integer.?

Question

Which of the following algebraic equations represents the following word problem.

The sum of three consecutive odd integers is 14 more than three times the 2nd integer.

x + (x+1) + (x+3) = 14 + 3(2x)

x + (x+2) + (x+4) = 14 + 3(x+2)

x + 1x + 3x = 14 + 3(x+2)

A + B + C = 14 + 3B

Answer 1

x + (x+2) + (x+4) = 14*3(x+2)


Assume that x is odd and it is the first integer.
Then the next ODD integer after x would be x+2, and the next one after that would be (x+2)+2 = x+4.

So our three conecutive odd integers are:
x, x+2, x+4

Sum indicates addition, so the first part of our equation is the three numbers added together:

x + (x+2) + (x+4)

The IS in the question indicates that the sum of the integers is EQUAL TO the next part of the statement.

14 more than three times the 2nd integer indicates:

14 + 3*(x+2)

since x+2 is the second integer.

Thus:
x + (x+2) + (x+4) = 14 + 3*(x+2)

Answer 2

Consecutive odd integers are two numbers apart:

1, 3, 5, 7, 9, 11, etc.

For any odd integer x, the next odd integer would be x+2, and the one after that would be x+4. That would be three consecutive odd integers.

Three times the 2nd integer would be 3(x+2). Add 14 to that, to get "14 more than" it.

Therefore, the answer is equation #2:

x + (x+2) + (x+4) = 14 + 3(x+2)

Answer 3

x + (x+2) + (x+4) = 14 + 3(x+2)

They are consecutive odd integers, meaning each one is 2 more than the last.

Let x be the first odd integer
Let x+2 be the second odd integer
Let x+4 be the third odd integer

So the final equation is:
x + (x+2) + (x+4) = 14 + 3(x+2)

Unfortunately, as given, there is no solution to this equation.
3x + 6 = 14 + 3x + 6
3x + 6 = 3x + 20
3x = 3x + 14
0 = 14 ?

Answer 4

Let the 3 integers be, respectively, 2n+1, 2n+3, 2n+5 with the last one being the greatest The sum should be 5 times the greates (2n+1) + (2n+3) + (2n+5) = 5(2n+5) where n is any integer that we need to solve for: 6n + 9 = 10n + 25 4n = -16 n = -4 The integers are: 2n+1 = 2(-4)+1 = -7 2n+3 = 2(-4)+3 = -5 2n+5 = 2(-4)+5 = -3

Answer 5

The secomd algebraic equation states it correctly. However, the answer is false. It is not possible for the left hand of the equation to be greater than three times the middle odd integer.

Answer 6

let the no.s be x , x+2, x+4 adding these you will get
3x+6=14+2x+4
x=12

Answer 7

The second one

Answer 8

first one