Question

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

Answer 1

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/}`