Question

? Re-express the following in “interval notation”, i.e., |x|<1 ⇒ −1< x <1. Draw the interval on a number line:

`| x - 3| < 1`

Answer 1

`2 < x < 4`

Explanation:

Follow the example you wrote in the question: if

`|x|<1 \implies -1 < x < 1`

then, by the same logic

`|x-3|<1 \implies -1 < x-3 < 1`

We may simplify the expression adding three everywhere:

`-1+3 < x-3+3 < 1+3`

`therefore 2 < x < 4`