### Video Transcript

Let the greatest element in a set
be 445 and the range of the set be 254. What is the smallest element of
this set?

We know that, in order to calculate
the range of any set, we subtract the smallest element from the largest element. In this question, we are given the
largest or greatest element and the range of the set and need to calculate the
smallest element. We can do this by using the formula
or by using the number line. Substituting in our values gives us
254 is equal to 445 minus 𝑥, where 𝑥 is the smallest element of the set. Adding 𝑥 to both sides of this
equation gives us 𝑥 plus 254 is equal to 445. We can then subtract 254 from both
sides of this equation to work out the value of 𝑥. 𝑥 is equal to 191 as 445 minus 254
is 191. We can therefore conclude that the
smallest element of the set is 191.

As already mentioned, we could also
have calculated this using a number line. We know that the greatest value is
445. The range is the difference between
the greatest or largest value and the smallest value. In this case, we are told it is
254. The difference between the smallest
and greatest value is 254, which means we can subtract this from 445 to calculate
the smallest value. Once again, this gives us an answer
of 191.