Question Video: Finding Three Consecutive Odd Numbers Whose Sum Is Nine | Nagwa Question Video: Finding Three Consecutive Odd Numbers Whose Sum Is Nine | Nagwa

# Question Video: Finding Three Consecutive Odd Numbers Whose Sum Is Nine Mathematics • First Year of Preparatory School

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The sum of three consecutive odd numbers is 9. If the first number is 2𝑥, find the value of 𝑥.

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### Video Transcript

The sum of three consecutive odd numbers is nine. If the first number is two 𝑥, find the value of 𝑥.

In this question, we are told that the sum of three consecutive odd numbers is nine. We want to find these three numbers and determine the value of 𝑥, given that the first of these numbers is two 𝑥.

To answer this question, we can start by recalling that the odd numbers are the integers that are not divisible by two. So they are numbers like negative three, negative one, one, three, and so on. We can also recall that consecutive odd numbers have a difference of two. In other words, the next odd number in the sequence is two larger than the previous.

It is possible to find these three consecutive odd numbers whose sum is nine by considering the list of odd numbers. However, we will see how to do this in general. Since the first number is two 𝑥, we can add two and then add two again to find the next two numbers in the list. Therefore, these three numbers are in the form two 𝑥, two 𝑥 plus two, and two 𝑥 plus four.

We can now add these three expressions together and note that their sum must be equal to nine. We can then simplify the left-hand side of the equation by collecting the like terms to get two plus two plus two times 𝑥 and then calculating that two plus four is six. Evaluating then gives us that six 𝑥 plus six is nine.

We can now solve the equation for 𝑥. We subtract six from both sides of the equation. This gives us that six 𝑥 equals three. Now, we can isolate 𝑥 by dividing both sides of the equation by six. We get that 𝑥 is equal to one-half. We can verify that this is correct by substituting 𝑥 equals one-half into our expressions for the three consecutive odd integers. We get one, three, five, which are all odd, consecutive, and their sum is nine, verifying that 𝑥 equals one-half.

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