How do you solve the inequality #abs(3x+5)+2<1# and write your answer in interval notation?

1 Answer
smendyka
Aug 20, 2017

See a solution process below:

Explanation:

First, subtract #color(red)(2)# from each side of the inequality to isolate the absolute value function while keeping the inequality balanced:

#abs(3x + 5) + 2 - color(red)(2) < 1 - color(red)(2)#

#abs(3x + 5) + 0 < -1#

#abs(3x + 5) < -1#

The absolute value function takes any number and transforms it into its non-negative form. Therefore, the result of an absolute value function cannot be negative and therefore cannot be #color(red)(< -1)#.

So, there is no answer to this question. Or, the answer is the empty or null set: #{O/}#

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