INEQUALITIES...!!! help?

Question

Solve the nonlinear ineqality. Express the solution using interval notation.

a) (x+2) (x-1) (x-3) < = 0

b) 1/x+1 + 1/x+2 < = 0

Answer 1

(x+2) (x-1) (x-3) < = 0
x+2 <= 0 --> x <= -2
x-1 < = 0 --> x <= 1
x-3 < = 0 --> x <= 3

(-Inf, 3]

1/x+1 + 1/x+2 < = 0
(x+1)(x+2)[1/x+1 + 1/x+2] < = 0
(x+2) + (x+1) < = 0
2x + 3 <= 0
2x <= -3
x <= -3/2

(-Inf, -3/2]

Answer 2

(-infinity, -2] U [1,3]
When x <-2 all three factors are negative so inequality holds
for - infinity
(-infinity, -2) U [-1.5, -1)