Question

PLease help me with this!

Answer 1

Answer:

1. x2 - 9 > 0

x^2-3^2>0

(x+3)(x-3)>0

(x+3)>0 and (x-3)>0

x>-3       and  x>3

2. x2 - 8x + 12 > 0

   x^2 - 8x  +12>0

   x^2 -2x -6x +12 >0   (-8x is replaced by (-2x) + (-6x) )

   x(x-2) -6(x-2) >0

    (x-6)(x-2)>0

(x-6)>0    and (x-2)>0

    x>6     and     x>2

3. -x2 - 12x - 32 > 0

    -x^2 -12x -32 >0

     x^2 +12x +32 <0

      x^2 +4x +8x +32<0

      x(x+4) +8(x+4)<0

      (x+8)(x+4)<0

(x+8)<0   and  (x+4)<0

x<-8      and    x<-4

4. x2 + 3x - 20 >= 3x + 5

   x^2 +3x -20 >= 3x +5

   x^2 +3x -20 -3x >= 3x +5 -3x

     x^2 -20  >= 5

     x^2 -20 +20  >= 5  +20

     x^2 >=25

     x^2-25 >=0

      (x-5)(x+5)>=0

(x-5)>=0  and (x+5)>=0

  x>=5    and x>=-5