Question

***WILL MEDAL***
What are the solutions to the equation 4x^3 - 5x = |4x|? List your answers in increasing order.

Answer 1

Absolute value is a by definition, the consideration of the negative and the positive regions of any given function, variable or expression.
Therefore, in order to take that away, you have to split the original equation, to the two following equations, and solve them independantly:
\[1) 4x^3-5x=(4x)\]
\[2)4x^3-5x=-(4x)\]

Answer 2

watch out for the domain true.
4x^3 - 5x = 4x if x > 0
and
4x^3 - 5x = -4x if x < 0

and if x = 0, then 0 = 0 (true), hence 0 is also one of the solutions

Answer 3

watch out for the domain *too*