How do you graph and solve #| 3x + 8 | +4 <=0#?

1 Answer
smendyka
Jul 17, 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 + 8) + 4 - color(red)(4) <= 0 - color(red)(4)#

#abs(3x + 8) + 0 <= -4#

#abs(3x + 8) <= -4#

However, the absolute value function takes any number and converts it to #0# or it's positive form. Therefore, the output of the absolute value function will always be #>= 0#.

So, the absolute value of #(3x + 8)# cannot be less than a negative number.

So, there is no answer to this problem.

Or, the answer is the null or empty set: #{O/}#

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