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3 Answers

First you want to get rid of the fraction number. Multiply each section of the compound inequality by 2:
 
2(-5)≤2(-3x+3/2)≤2(3)
-10≤-6x+3≤6
 
Now you want to isolate the x in the middle so subtract 3 from every part of the compound inequality:
 
-10-3≤-6x+3-3≤6-3
-13≤-6x≤3
 
Now divide every part by -6 - Remember that when you divide by a negative you have to switch the greater than or equal signs to less than or equal!
 
-13/-6≤-6x/-6≤3/-6
13/6≥x≥-1/2
 
Interval notation for this answer is [-1/2, 13/6]. If you need more help understanding interval notation, refer to this website: http://www.coolmath.com/algebra/07-solving-inequalities/03-interval-notation-01.htm
-5<-3x+3/2<3
2(-5)<2[-3x+3/2]<2(3)
-10<-6x+3<6
-10-3<-6x+3-3<6-3
-13<-6x<3
 13>6x>-3
-3<6x<13
-1/2<x<2 1/6
-5≤-3x+(3/2)≤3
First keep the variable alone so we will subtract 3/2 from all 3 sides of ineq.
 
-5-(3/2) ≤ -3x  ≤ 3-(3/2)
 
-6.5≤ -3x≤1.5
divide all sides by -3 so you MUST FLIP THE SIGNS
 
13/6 ≥x≥-(1/2)
or
   -1/2  ≤x ≤13/6