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

1 Answer
Aug 2, 2017

Answer:

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)#

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