How do you solve and write the following in interval notation: # |x-1|-4>=5#?

1 Answer
Alan P.
Jun 15, 2016

#x in {(-oo,8],[10,+oo)}#

Explanation:

#abs(x-1)-4 >= 5#

#rArr abs(x-1) >= 9#

This breaks down into 2 cases:
#{: ("if "x < 1,color(white)("XXXXXXXX"),"if " x >=1), (color(white)("XX")1-x >=9,,color(white)("XX")x-1 >= 9), (color(white)("XX")-x >= 8,,color(white)("XX")x>=10), (color(white)("XX")x <= -8,,) :}#

So we have
#color(white)("XX")#either #x <= -8#
#color(white)("XX")#or #color(white)("XX")x >=10#

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