Question

How do you solve `|t - 9| > 9`?

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.

`-9 > t - 9 > 9`

Add `color(red)(9)` to each segment of the system of inequalities to solve for `t` while keeping the system balanced:

`-9 + color(red)(9) > t - 9 + color(red)(9) > 9 + color(red)(9)`

`0 > t - 0 > 18`

`0 > t > 18`

Or

`t < 0` and `t > 18`

Or. in interval notation:

`(-oo, 0)` and `(18, +oo)`