How do you solve #-4 <= 1/3x-5<-2#?

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Answer 1 · 2015-04-28T22:40:36

Solution: #3<=x<9#

To begin with, notice there are two inequalities you've got to solve, which are:
#4<=1/3x-5# and #1/3x-5<-2#

No 1

#-4<=1/3x-5#

This is the same as #x/3-5>=-4#

#=>x/3>=-4+5 => x/3>=1 => x>=3#

No 2

#1/3x-5<-2 => x/3<-2+5 => x/3<3 => x<9#

Now, combine the two inequalities,

#=> x>=3, x<9#

This means that #3<=x<9#