Solve each inequality Write your answer using interval notat

Solve each inequality. Write your answer using interval notation. (If you need to use -infinity -4

Solution

9)

a)

-4<5-3x<=17

-4-5<5-3x-5<=17-5

-9<-3x<=12

-12<=3x<9

-12/3<=3x/3<9/3

-4<=x<3

[-4,3)

b)x^2<2x+8

x^2 -2x -8<0

(x-4)(x+2)<0

x+2>0,x-4<0

x>-2,x<4

(-2,4)

c)x(x-1)(x+2)>0

sign chart

............-2..........0...........1...................
.....--.............+.........--...........+

(-2,0)U(1,)

d)|x-4|<3

-3<x-4<3

-3+4<x-4+4<3+4

1<x<7

(1,7)

e)(2x-3)/(x+1)<=1

(2x-3)<=(x+1)

2x-x<=1+3

x<=4

(-,4]