Solve please

Question

Solve the compound inequality. Type your answer in interval notation. Simplify your answer.

 

-5≤-3x+3/2≤3

Answer 1

-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

Answer 2

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

Answer 3

-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