I hope someone can help. I'm trying to solve for the following question:

*<= "less than or equal to"*__>= "greater than or equal to"__

These are my steps:

1. I know that the volume of a rectangle is l x w x h - therefore the inequality to the equation must be

**x(50 - 2x)(30 - 2x) <= 4000**, where x represents the height, 50 - 2x represents the width, and 30 - 2x represents the length.

2. Find the roots to the inequality: x = 0, x = 25, and x = 15

3. Create intervals for the corresponding roots: x <= 0, 0 <= x <= 15, 15 <= x <= 25, x >= 25

4. Identify values within those intervals, then sub those intervals within the inequality equation. If the outcome is less than or equal to 4000, then consider this a range of the side lengths. These ranges would represent my solution(s) to this question.

**The textbook solution 5 < x < 7.19. My solution is wrong so I would appreciate some guidance on where I went wrong in my steps.**

Sincerely,

Olivia