Solve the compound inequality. Type your answer in interval notation. Simplify your answer. -5≤-3x+3/2≤3 Oct 11 | Theresa from Jackson, NJ | 3 Answers | 0 Votes Mark favorite Subscribe Comment
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 Oct 11 | Erica M. Best answer Comment
-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 Oct 11 | Arthur D. Comment
-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 Oct 11 | Adel E. Comment