For this case we have the following inequality:
[tex]|x-2| - 1 \ \textgreater \ 2[/tex]
We can rewrite the inequality as follows:
[tex]|x-2| \ \textgreater \ 2 + 1[/tex]
[tex]|x-2| \ \textgreater \ 3[/tex]
From here, we have two possible cases:
Case 1:
[tex]x-2 \ \textgreater \ 3[/tex]
Case 2:
[tex]x-2 \ \textless \ -3
[/tex]
Therefore, graphically, it is observed that the solution is:
(5, ∞)
(-∞, -1)
To do this, we must observe the shaded region in the graph, or equivalently the numerical line.
Answer:
(5, ∞)
(-∞, -1)
See attached image for the graphic solution
