The length of a box is 4 inches longer than its width, and the height is 2 inches shorter than the width. Which equation can you use to solve for the length of the box if the volume is 240 cubic inches? (Assume that the width of the box is x.)

width ---- x

length --- x+4
height ---x-2

x(x+4)(x-2) = 240
x(x^2 + 2x -8) = 240
x^3 + 2x^2 - 8x - 240 = 0

after a few trials, I found x = 6 to work.

( tried x=3,4,5,6 , no need to try any negatives or x<2)

Auper

To solve for the length of the box, we can start by assigning variables to the given information:

Let x be the width of the box.

The length of the box is 4 inches longer than its width, so the length would be x + 4.

The height is 2 inches shorter than the width, so the height would be x - 2.

The formula for the volume of a rectangular box is length x width x height.

Therefore, the equation to solve for the length of the box when the volume is 240 cubic inches is:

(x + 4) * x * (x - 2) = 240

To solve for the length of the box, let's first set up the equation based on the given information:

The length of the box is 4 inches longer than its width, so the length can be represented as (x + 4).

The height of the box is 2 inches shorter than the width, so the height can be represented as (x - 2).

Since we have the width (x), length (x + 4), and height (x - 2), we can calculate the volume of the box by multiplying these values together:

Volume = Length × Width × Height

240 = (x + 4) × x × (x - 2)

The equation we can use to solve for the length of the box is:

240 = x(x + 4)(x - 2)