Question

How do you solve and write the following in interval notation: `-8< -2x – 1 ≤ -5`?

Answer 1

`[2,7/2)`

Explanation:

Remember, we want only an `x` in the middle on the inequality, so whatever we do, we must to it to all three parts.

We can start by adding `1` to all three parts to get

`-7<-2x<=-4`

To get just an `x` in the middle, we can divide all parts by `-2`. Recall that dividing or multiplying by a negative flips the signs. We get

`7/2>x>=2`, which is the same as `2<=x<7/2`. In interval notation, we can write this as

`[2,7/2)`

Note that the bracket means we include the bound, and the parenthesis means we don't include it.

This is the same as saying all values between `x=2` and `x=7/2`, including `2` and not including `7/2`.

Hope this helps!