This problem is best understood with reference to White's opportunities (see /Solution - White). White has two major sente plays, in the upper left and upper right. The upper left play threatens the life of the black stones but is only three points different from a black play. The upper right is therefore the larger play.
Black could play hane at 4 instead of 3. But since he has to play 3 and 5 and then connect twice (at 6 and 7), he can not win the resulting ko so there is no point.
Black has 31 points to White's 28. This time B+3.
Nothing to add, since this is indeed the correct solution.