Question #23a85

1 Answer
KillerBunny
Oct 6, 2016

#|m-15|<4#

Explanation:

An absolute value inequality holds when a certain variable is bounded symmetrically with respect to zero, i.e. it ranges from #-k# to #k#, for some real number #k#.

For example. if you have #-8<x<8#, then you can say that #|x|<8#.

In your case, we need to subtract from all members a certain quantity, so that the foretold symmetry holds.

For example, if we subtract #11# from all sides, we have

#11-11<m-11<19-11#, and thus

#0<m-11<8#

From here, we can see that we need to subtract #4# more to make the range symmetric:

#-4<m-15<4#, and thus #|m-15|<4#

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