Question

How do you solve and write the following in interval notation: `2x - (7 + x) <= x`?

Answer 1

`x in (-oo, oo)`

Explanation:

`2x - (7+x) <= x`

`=> 2x - 7 - x <= x`

`=> x - 7 <= x`

`=> -7 <= 0`

As the above is a tautology (always true, regardless of the value of `x`), the solution set is all real numbers. In interval notation, we can write this as having the endpoints of `+-oo`:

`x in (-oo, oo)`