Question

Help please, with explanation

Answer 1

D.
`x<-6\mbox{ or } x>2`

Explanation:

`|x+2|-1>3`

First, add 1 to both sides:

`|x+2|>4`

Now, you can split this into 2 equations. The value of the absolute value statement will be the same whether the statement inside is positive or negative. Example:

`|2|=2\\|-2|=2`

Because of that, the
`x+2` could be positive or negative and still be true.

`x+2>4\\-(x+2)>4`

Then, you can solve both of these inequalities. Top one here:

`x+2>4\\x>2`

Bottom one:

`-(x+2)>4`

Divide both sides by a -1 here, but be sure to invert the inequality sign:

`x+2<-4\\x<-6`

The solutions are:

D.
`x<-6\mbox{ or } x>2`