... assume that a1≥ a2≥ ≥ anand b1≥ b2≥ ≥ bn. Because () is true for all x ∈ R, if we choose x ≥ max{ai,bi}ni=1thenni=1|ai− x| = nx −ni=1ai;ni=1|bi− x| = ... nx −ni=1bi;⇒ a1+ a2+ + an≤ b1+ b2+ + bn.www.VNMATH.com6Similarly, if we choose x ≤ min{ai,bi}ni=1, thenni=1|ai− x| = −nx +ni=1ai;ni=1|bi− x|...