Question

How do you express intervals as inequalities such as [-2,9]?

Answer 1

`[-2,9]` is written as the inequality `-2<=x<=9`

Explanation:

The expression `[-2,9]` in interval form means that

the concerned variable, say `x` has a lower limit of `-2` and including `-2`, as we have square brackets but had we parentheses i.e. '`(`', this means that `-2` is not included.

In other words `x>=-2` as value of `x` is not less than `-2`.

Further, as the interval has an upper limit of `9`, again including `9`, as we have square brackets but had we parentheses i.e. '`(`', this means that `9` is not included.

In other words `x<=9` as value of `x` is not greater than `-2`.

The two limits can then be combined as `-2<=x<=9`

Note that had it be `(-2,9)`,

the result would have been `-2 < x < 9`.

`(-2,9]` as `-2 < x <= 9`

and `[-2,9)` as `-2 <= x < 9`