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.
