Question

The sum of 4 consecutive odd integers is equal to zero. Write an equation to model the sentence. Solve the equation to find the numbers. Check your solution.

Answer 1

Answer:

  {-3, -1, 1, 3}

Step-by-step explanation:

Sometimes it is convenient to consider the average value of the integers in a "consecutive integer" problem.

Setup

We know the average value of 4 consecutive odd integers is the even integer between the middle two. If we call that "n", then the integers of interest are (n-3), (n-1), (n+1), and (n+3). Of course, their sum is 4 times the average value, so is 4n.

  4n = 0 . . . . . . the sum of the 4 consecutive odd integers is 0

Solution

Dividing by 4, we find the average value to be ...

  n = 0/4 = 0

Then the 4 integers are ...

• n -3 = 0 -3 = -3
• n -1 = 0 -1 = -1
• n +1 = 0 +1 = 1
• n +3 = 0 +3 = 3

Check

The average is the sum, divided by the number of contributors:

  0 = (-3 +(-1) +1 +3)/4 = 0/4 . . . . . . true

Answer 2

The equation that models the sentence is : x + (x + 2) + (x + 4) +  (x + 6)  = 0. The numbers are {-3, -1, 1, 3}.

An odd number is a number that cannot be divided into half without any remainders. For example when 7 is divided in half, its value is 3.5. Examples of Positive odd numbers are 1,3, 5, 7. 11 etc. Examples of Negative odd numbers are -1, -3, -5, -7 etc.

What are Consecutive Odd Numbers?

Consecutive odd numbers are odd numbers that follow each other. Examples are 1, 3, 5. Consecutive odd numbers increase/decreases by 2.

In order to model the sentence, let x represent the first odd number then

Second odd number = x + 2

Third odd number = x + 4

Fourth odd number = x + 6

The equation is: x + (x + 2) + (x + 4) + (x + 6)  = 0

{ put x = -3 } we get {-3, -1, 1, 3} numbers. Here,

First odd number = -3

Second odd number = -1

Third odd number = 1

Fourth odd number = 3

When we put {-3, -1, 1, 3} values in the above equation then,

such that: (-3) + (-1) + 1 + 3 = 0.

Hence, The equation that models the sentence is : x + (x + 2) + (x + 4) +  (x + 6)  = 0 and the numbers are {-3, -1, 1, 3}.

Learn more about "Consecutive Odd Numbers" from here: brainly.com/question/15453368

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