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

1 Answer
Oct 9, 2017

Answer:

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)#