Given |a−b|=2| and |b−c|=5, let S be the set of all possible values of |c−a|. What is the sum of all elements of S?

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Answer 1 · 2017-12-10T21:06:07

10

if #|a-b|=2#
then #a-b = 2 or -2#

if #|b−c|=5#
then #b-c=5 or-5#

adding the two equations,

#a-c=7,3,-3 and 7#

thus #c-a=-7,-3,3, and 7#

therefore, #|c-a|=7 and 3#

#S=7 and 3#

#7+3=10#