how to solve the inequality in terms of intervals
(x+3)(x-8)(x+8)and = 0

Question

how to solve the inequality in terms of intervals 
(x+3)(x-8)(x+8)>and = 0

myininaya · Answer

(x+3)(x-8)(x+8)=0 when x=3 or when x=8 or when x=-8

----|----|---|----
      -8    3      8

you have four intervals to test

myininaya · Answer

oops x=-3 or x=8 or x=-8

myininaya · Answer

---|---|---|---
    -8   -3   8

these are the intervals we will test:
$$(-\infty,-8);(-8,-3);(-3,8);(8, \infty)$$

myininaya · Answer

$$f(x)=(x+3)(x-8)(x+8)$$

$$f(-9)=(-9+3)(-9-8)(-9+8)=(-)(-)(-)=-$$$$f(-4)=(-4+3)(-4-8)(-4+8)=(-)(-)(+)=+$$
$$f(0)=(0+3)(0-8)(0+8)=(+)(-)(+)=-$$
$$f(9)=(9+3)(9-8)(9+8)=(+)(+)(+)=+$$

myininaya · Answer

we want f>=0
its 0 when w have -8,-3,8
and bigger than 0 when we have (-8,-3) or (8,inf)
so the answer is
$$[-8,-3] \cup [8,\infty)$$

anonymous · Answer

is question asking fx? 
In fact , I have not done math practice for 15 years.