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

1 Answer
Sep 25, 2017

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)#