Question

How do you solve and write the following in interval notation: `2 < 2x + 4 < 10`?

Answer 1

`(-1,3)`

Explanation:

As `2 < 2x+4 <10`

we have `2 < 2x+4` or `2-4 < 2x` i.e. `-1 < x`

Further, as `2x+4 < 10`, we have `2x < 6` or `x < 3`

Hence we have `-1 < x < 3`,

which in interval notation can be written as `(-1,3)`

Note: Had it been `-1 <= x < 3`, we would have written `[-1,3)` i.e. for inequality with equality we use square brackets and for pure inequality we use small brackets.