# SOLUTION: what are the answers for the following: -4<3x+1<=10 -2<=3x+8<-17 9>6-a -6x+3<=-32

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 Question 30023: what are the answers for the following: -4<3x+1<=10 -2<=3x+8<-17 9>6-a -6x+3<=-32Answer by sdmmadam@yahoo.com(530)   (Show Source): You can put this solution on YOUR website!1)-4<3x+1<=10 ----(1) 1)-4<3x+1 -4-1 < 3x (grouping like terms) -5 < 3x Dividing by 3 and division by a positive quantity does not alter the inequality and so here less than remains less than (-5/3) < x ----(*) 3x+1<=10 3x <= 10-1 3x <= 9 Dividing by 3 x <= 3 ----(**) From (*) and (**) we have (-5/3) < x <= 3 2)-2<=3x+8<-17 ----(2) -2<=3x+8 -2-8 <= 3x -10<= 3x Dividing by 3 and division by a positive quantity does not alter the inequality and so here less than remains less than (-10/3) <= x ----(1) 3x+8<-17 3x < -17-8 Dividing by 3 x < -25/3 ----(2) But by (1), x is to the right of (-10/3) and that which is to the right of (-10/3) CANNOT be to the left of (-25/3) Please draw a horizontal line and mark O on it to represent the number zero. This line is your number line. Go 3 and (1/3) units to the left of O and mark A on this line. Go still left and mark B on this line such that OB =8 and (1/3) that is B is 5 units to the left of A. Now you can see,feel and understand how the two possibilities for x are contradictory. So no solution. That is the answer set is the empty set. 3)9>6-a a > 6-9 (grouping like terms,changing sign while changing side) a > -3 4)-6x+3<=-32 -6x <= -32-3 -6x <= -35 x >= (-35)/(-6) Dividing by (-6) and division by a negative quantity alters the inequality and so here less than becomes greater than. That is x >= 35/6