Question

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

Answer 1

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/}`