½(b-3)- (½-b)=b+3

Using the distributive property:

½b - 3/2 - ½ + b  =  b + 3

To get rid of the denominators, multiply each term times 2:

  b - 3 - 1 + 2b  =  2b + 6

             3b - 4  =  2b + 6

Subtract 2b from both sides:

               b - 4  =  6

                    b  =  10