How do you solve -4 <= 1/3x-5<-2−4≤13x−5<−2?

1 Answer
Antoine
Apr 28, 2015

Solution: 3<=x<93≤x<9

To begin with, notice there are two inequalities you've got to solve, which are:
4<=1/3x-54≤13x−5 and 1/3x-5<-213x−5<−2

No 1

-4<=1/3x-5−4≤13x−5

This is the same as x/3-5>=-4x3−5≥−4

=>x/3>=-4+5 => x/3>=1 => x>=3⇒x3≥−4+5⇒x3≥1⇒x≥3

No 2

1/3x-5<-2 => x/3<-2+5 => x/3<3 => x<913x−5<−2⇒x3<−2+5⇒x3<3⇒x<9

Now, combine the two inequalities,

=> x>=3, x<9⇒x≥3,x<9

This means that 3<=x<93≤x<9

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