Write the absolute value equation representing all numbers x whose distance from 4 is 8 units.?

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Answer 1 · 2018-06-08T06:39:58

#abs(x-8)=4#
#x= {-4, 12}#

We are told that #x# is the set of numbers such that the distance from #x# to #4# is #8# - We'll assume #x in RR#

The distance of #x#, positive or negative, from 4 can be expressed as #abs(x-4)#

Since this distance is equal to #8# our equation is:

#abs(x-4) =8#

To solve for #x#:

Either +(x-4) = 8 -> x=12#

Or -(x-4) = 8 -> x=-4#

Hence, set #x ={-4, 12}#