Question

How do you solve and write the following in interval notation: `x <2` OR `x > 1`?

Answer 1

`x<2" "OR" "x>1hArr(-oo,oo)`

Explanation:

`x<2` means `x` can take any value less than two and interval notation, this means `(-oo,2)`, meaning that all numbers between `-oo` and `1` are included and as `-oo` and `2` are not included we have use small brackets. This forms one set of numbers, say `P`.

`x>1` means `x` can take any value greater than one and interval notation tis means `(1,oo)` , meaning that all numbers between `1` and `oo` are included, but not `13` and `oo`. This forms another set of numbers, say `Q`.

Hence `x<2" "OR" "x>1` represents the union of two sets `P` and `Q` i.e `PuuQ` or in other words `(-oo,2)uu(1,oo)`.

Observe that `PuuQ` includes all the numbers from `-oo` to `oo` and hence `x<2" "OR" "x>1hArr(-oo,oo)`