How do you solve #|-3x-7|+4<3#?

1 Answer
smendyka
Jun 9, 2017

See a solution process below:

Explanation:

First, subtract #color(red)(4)# from each side of the inequality to isolate the absolute value function while keeping the inequality balanced:

#abs(-3x - 7) + 4 - color(red)(4) < 3 - color(red)(4)#

#abs(-3x - 7) + 0 < -1#

#abs(-3x - 7) < -1#

The absolute value function takes any negative or positive term and transforms it to its positive form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Therefore, there is no solution to this problem which will allow the absolute value function to be less than #0# therefore it cannot be less than #-1#

There is no solution to this problem or the solution is the empty or null set: #{O/}#

Related questions
Impact of this question
801 views around the world
You can reuse this answer
Creative Commons License