Question

How do you solve and graph `abs(t+6)>4`?

Answer 1

See a solution process below:

Explanation:

The absolute value function takes any negative or positive 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.

`-4 > t + 6 > 4`

Subtract `color(red)(6)` from each segment of the system of inequalities to solve for `t` while keeping the equation balanced:

`-4 - color(red)(6) > t + 6 - color(red)(6) > 4 - color(red)(6)`

`-10 > t + 0 > -2`

`-10 > t > -2`

Or

`t < -10` and `t > -2`

Or, in interval notation:

`(-oo, -10)` and `(-2, +00)`