This is a simple problem of ranges, we will find that the ranges for the main floor and the balcony are:
[-6ft, 8ft] or {x ∈ R | -6ft ≤ x ≤ 8ft}
[26ft, 37ft] or {x ∈ R | 26ft ≤ x ≤ 37ft}
respectively.
We know that:
The main floor of the auditorium ranges from 6ft below the stage to 8 feet above the stage.
The floor of the balcony ranges from 26 to 37 feet above the stage
The ranges relative to the stage will be, in interval notation, the interval that contains the two extremes of the range.
For the main floor, it goes from -6ft to 8ft (the first one is negative because is 6ft below the stage) then this interval will be: [-6ft, 8ft]
While in set-builder notation we want to specify that the variable must be a real number, so we start with: {x ∈ R
And we need to specify that x can go from -6ft to 8ft, then we add the restriction:
{x ∈ R | -6ft ≤ x ≤ 8ft}
Notice that we use a close interval here.
While for the balcony, the minimum is 26ft and the maximum is 37ft, then the interval will be [26ft, 37ft]
For the set-builder notation we will have:
{x ∈ R | 26ft ≤ x ≤ 37ft}
If you want to learn more, you can read:
https://brainly.com/question/19159374
