Question

Solve the inequality: x(x-4)^2 (x-9)^3 > 0

Answer 1

forget the \((x-4)^2\) term since it is always positive unless\(x=4\) in which case it is 0

Answer 2

and \((x-9)^3\) has the same sign of \(x-9\)

Answer 3

so you can start by solving
\[x(x-9)>0\]

Answer 4

why can you disregard the cube in x(x-9)

Answer 5

because \(x^3>0\iff x>0\) and similarly \((x-9)^3>0\iff x-9>0\)

Answer 6

the cube of a number has the same sign as the number

Answer 7

well my teacher wants me to solve it by changing the inequality to an = sign