Question

How do you solve and write the following in interval notation: `-5<5+2x<11`?

Answer 1

`x in (-5,3)`

Explanation:

You can add/subtract both sides of an inequality without changing the orientation of the inequality;
you can also multiply or divide both (all) sides of an inequality by a value greater than zero without changing the orientation of the inequality..

Given: #-5 < 5 +2x <11

subtract `5` from each "side
`-10 < 2x < 6`

divide each "side" by `2`
`-5 < x < 3`

Answer 2

`-5 < x < 3` or in interval notation: `x in (-5, 3)`

Explanation:

Break the question into two inequalities and solve each separately.

LHS: keep x term on the right but on the RHS keep x term on left

`-5 < 5 + 2x " and " 5 + 2x <11`

`-5 -5 < 2x " " 2x < 11-5`

`-10 <2x " " 2x < 6`

`-5 < x " " x < 3`

But the x terms are the same term, so the two parts can be combined:

`-5 < x < 3`