In this chapter, we discuss ideas for partially solving the Aleksandrov-Rassias problems using the inequalities presented in Chap. 6 . In the first section, we partially solve the Aleksandrov-Rassias problems by using the inequality for the distances among six points presented in Sect. 6.1 . Section 7.2 is devoted to proving that any mapping between real Hilbert spaces whose dimensions are greater than 2 is an affine isometry if the distance 1 is preserved, \(\frac {1}{\sqrt {2}}\) is contractive, and when \(\sqrt {3}\) is extensive. In Sect. 7.3, we give a partial solution to the Aleksandrov-Rassias problems by proving that when the distance 1 is contractive and the golden ratio is extensive by a mapping defined between real Hilbert spaces and when the dimension of its domain is greater than 2, then this mapping is an affine isometry. In the last section of this chapter, we prove that a mapping between real Hilbert spaces whose domain has the dimension greater than 2 is an affine isometry if the distances 1 and \(\alpha \) are contractive, \(\beta \) is extensive, and if the distances 1, \(\alpha \) and \(\beta \) satisfy some suitable conditions. The main results presented in this chapter have been extracted from the papers by Jung (Nonlinear Anal 62(4):675–681, 2005); Jung and Lee (J Math Anal Appl 324(2):1363–1369, 2006); Jung and Nam (J Math Inequal 12(4):1189–1199, 2018); Jung and Nam (J Math Inequal 13(4):969–981, 2019) and explained in detail so that the reader can easily understand them.