Question

solve |x-1/2|>3

Answer 1

as written the solution is \[x<\frac{-5}{2}\text{ or }x>\frac{7}{2}\]

Answer 2

it use [] to represent the absolute value for convenience.
[x-0.5]>3
so in this case, x-0.5 must be numerically greater than 3. (numerically means regardless of its sign)
x-0.5 must be greater than 3 or lower than -3 in order to achieve this.
x>3.5 or x<-2.5

Answer 3

Solution is:
Re(x)>7/2 and Re(x)<-5/2