Final answer:
Values of x that satisfy the equation can be found by converting the equation to a polynomial and then using algebraic methods. Some obtained values may need to be discarded based on context.
Step-by-step explanation:
The student has asked to identify all values of x that make the equation x - 3/x = -8/(x³) true. To solve this, the equation can be transformed into a polynomial equation by multiplying through by x³, which will then allow use of the quadratic formula or factoring to find the potential values for x. However, it is important to note that in some contexts, certain values of x may not be possible due to physical constraints or the nature of the problem, such as negative concentrations in a chemical reaction.
By carefully evaluating the resultant values for x, we can discard the values that do not make sense in the given context, leaving us with the viable solution.