Question

The sum of 4 odd integers is equal to zero

A.Write an equation to model the sentence

B.Solve the equation to find the numbers. Check your solution

Answer 1

A. The equation can be written as:

x + y + z + w = 0

Explanation:

B. To solve the equation and find the numbers, we need to consider the properties of odd integers. Odd integers can be written as 2n+1, where n is any integer.

Substituting 2n+1 for each variable in the equation, we get:

(2n+1) + (2n+1) + (2n+1) + (2n+1) = 0

Simplifying the equation:

8n + 4 = 0

8n = -4

n = -4/8

n = -1/2

Substituting the value of n back into the equation, we find the values of the four odd integers:

x = 2(-1/2) + 1 = 0

y = 2(-1/2) + 1 = 0

z = 2(-1/2) + 1 = 0

w = 2(-1/2) + 1 = 0

Checking the solution, we can see that when we add these four numbers, we get:

0 + 0 + 0 + 0 = 0

Therefore, the solution to the equation is x = y = z = w = 0.