Question

How do you solve and write the following in interval notation: `2x> -10` or `x > 1`?

Answer 1

`(-5,\infty)`

Or, if you want to look cool and smart,

`x in (-5, \infty)`

Explanation:

Simplifying the first inequality:

`2x > -10`
`x > -5`

Note that the second inequality is contained within the first inequality; if `x` is greater than 1, then it must also be greater than -5. Thus, we can just ignore the second inequality.

Putting this into interval notation, the lower bound would be -5, without including -5, and the upper bound is `\infty`:

`x in (-5, \infty)`

The left parentheses is round, since we are excluding -5. The right parentheses is also round, because of convention (and also because infinity is just a concept and not an actual number)

The fancy "E" represents the word "in"; `x in [a, b]` means that `x` is in the interval `[a, b]`.