The given inequality is
[tex]2>|x-1|[/tex]
This inequality is equivalent to
[tex]|x-1|<2[/tex]
We use the following absolute value properties for inequalities
[tex]|x|Applying this property, we have[tex]|x-1|<2\rightarrow-2Now, we have a compound inequality, let's solve it[tex]\begin{gathered} -2This means the solution set is
all real numbers greater than -1 but less than 3. The following graph described this solution.
Therefore, the right answer is the second option.
