Algebra 2 question

Question

the volume v (in cubic inches) of a rectangular cardboard box is modeled by the function v(x)= (18-2x)(3-2x)x, where x is the width (in inches) of the box. Determine the values of x for which the model makes sense. Explain your reasoning.

Answer 1

Since x represents the width, it clearly must be greater than zero since a box must have each dimension be positive which makes the lower bound. The question is whether 18-2x and 3-2x represent the other 2 dimensions or not.

If so, then 3-2x must also be greater than zero which makes the possible range of x as 0<x<1.5

If not, then in addition to the above range, values of x such that both 3-2x and 18-2 evaluate to negative still result in a positive volume. Therefore, additional values of x are x>9.