Question

How do you solve and write the following in interval notation: `7 ≤ x + 4` or `x - 1 ≥ 5`?

Answer 1

First, solve each inequality separately:

`7<=x+4`
`:.7-4<=x+4-4`
`:.3<=x`
`:.x>=3`
`x` can be any value between `3` (including) and `oo`. Therefore, `x in [3,oo)`. Brackets mean that it is included, while parentheses mean that it is not included. `oo` is never included for interval notations.

`x-1>=5`
`:.x-1+1>=5+1`
`:.x>=6`
`x` can be any value between `6` (including) and `oo`. Therefore, `x in [6,oo)`.

We can combine these two to get `x in [3,oo) nn [6,oo)`. This is equivalent to `x in [6,oo)`.