Question

How do you solve and write the following in interval notation: `|x-4| >2`?

Answer 1

See a solution process below:

Explanation:

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

`-2 > x - 4 > 2`

Add `color(red)(4)` to each segment of the system of inequalities to solve for `x` while keeping the system balanced:

`-2 + color(red)(4) > x - 4 + color(red)(4) > 2 + color(red)(4)`

`2 > x - 0 > 6`

`2 > x > 6`

Or

`x < 2` and `x > 6`

Or, in interval notation:

`(-oo, 2)` and `(6, +oo)`