Question

How do you solve and write the following in interval notation: `-3 ≤ (x − 4) / 2 <4`?

Answer 1

`x` will be in the interval `[-2, 12)`.

Explanation:

When manipulating an inequality, we can treat it as a three part equation. Whenever we alter one part, we do the same to the other two. This allows us to manipulate the equation like so:
`-3 ≤ (x − 4) / 2 < 4`
`-6 ≤ x − 4 < 8`
`-2 ≤ x < 12`

So the final answer is that `x` will be in the interval `[-2, 12)`.

Answer 2

`x in[-2,12[`

Explanation:

First, you can multiply all terms by 2:

`-6<=x-4<8`

and then you can add 4 to all terms:

`-2<=x<12`