Question

Question #97418

Answer 1

`x=-3`

Explanation:

We want to solve `|3x+2|>4` first.

`3x+2>4` or `-(3x+2)>4`

For `3x+2>4 rightarrow3x>2rightarrow x>2/3`. Only positive values work there, so it's not helping us with this problem.

For `-(3x+2)>4 rightarrow 3x+2<-4`

`3x<-6 rightarrow x <-2`.

So any number less than `-2` will work.

On the number line numbers are bigger when they are to the right of other numbers, which is important to keep in mind with negative numbers.

Since `x<-2`, the largest negative integer that works is `x=-3` because it is the farthest to the right of all possible negative integers that work.