Question

How do you write: the sum of number and three no more than eight or is more than twelve of?

Answer 1

`n <= 5color(white)("XX")orcolor(white)("XX")n>9`
`color(white)("XXX")`or
`n cancel(in) (5,9]`

Explanation:

Let the number be represented by `n`

sum of number and three:
#color(white)("XXX")n+3

(sum of number and three) no more than eight:
`color(white)("XXX")n+3 <= 8`

Here is where things get a bit unclear:
- is it the "number plus three" that is more than twelve?
or just "the number" that is no more than twelve.
- what is the significance of "of" in "twelve of"?
I will interpret this as:
`color(white)("XXX")n+3 > 12`

So we have as a combination:
(sum of number and three no more than eight)
or
(sum of number and three more than twelve)
`color(white)("XXX")n+3 <=8color(white)("XX")orcolor(white)("XX")n+3 > 12`

This could be simplified to
`color(white)("XXX")n <= 5color(white)("XX")orcolor(white)("XX")n > 9`

Note that this can not be written as a single algebraic inequality
but it could be written using a set of ranges:
`color(white)("XXX")n in {(-oo,5], (9,+oo)}`
or
`color(white)("XXX")n cancel(in) (5,9]`