How do you solve and write the following in interval notation: #|x + 7| ≥ 2 #?

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Answer 1 · 2016-07-10T04:29:04

#x in ]-oo,-9] uu [-5,+oo[#

Since #|f(x)|>=k# is equivalent to:

#f(x)<=-k or f(x)>=k#,

in this case you can solve:

#x+7<=-2 or x+7>=2#

#x<=-2-7 or x>=2-7#

#x<=-9 or x>=-5#

or #x in ]-oo,-9] uu [-5,+oo[#