Question

Find the interval equivalent to 2 < x ≤ 5 or x >7

Answer 1

`(2,5]\cup(7,\infty)`

For inequality symbols less than < or greater than >, we will use round parenthesis ( or )

For inequality symbols less than or equal to ≤ and greater than or equal to ≥, we will use brackets [ or ]

When combining intervals with "or", we will use ∪.

For the given inequality:

2 < x ≤ 5 or x >7

Since we used < for 2, we will use parenthesis (

We used ≤ for 5, hence we will use bracket ]

Combined with "or", we will use ∪

Since we used > for 7, we will use parenthesis (

And since x is any value greater than 7 and could go on until positive infinity, we will use ∞ and parenthesis )

The interval equivalent to this would then be:

`(2,5]\cup(7,\infty)`