(x-8)(x-1)^2(x+4)<0

Question

solve for x

Answer 1

Mark's analysis is great EXCEPT that zero is neither a positive nor a negative number. The. complete idea of a positive and negative number is to focus on zero. Negative numbers are the numbers that are less than zero. If (number<0) then the number is a negative number. Positive numbers are the numbers that are greater than zero.

(x-1)^2 may be 0 when x=1. This makes the answer:

x such that -4<x<1 and 1<x<8

Answer 2

(x - 1)² is always positive.

For the product to be negative, < 0, either

x - 8 < 0 and x + 4 > 0

or

x - 8 > 0 and x + 4 < 0

x - 8 < 0 and x + 4 > 0

x < 8 and x > -4

This is possible

x - 8 > 0 and x + 4 < 0

x > 8 and x < - 4

This is not possible

{x | -4 < x < 8}