I feel like the answer in my book is incorrect. If someone could verify this it would be greatly appreciated. Here's the original problem: "The cost, $C, of producing x units of a product is given by the function C = 2000 + 4x, up to a cost of $10,000. Find the range. The book had the answer 0 ≤ C ≤ 10,000 while I got the answer of 2,000≤C≤10,000

Question

accessdenied · Answer

How did you get your answer?

anonymous · Answer

I calculated the range by realizing 0 is the smallest real number that can possibly plugged in for the x value, so for the C value(range) it shows that the smallest possible number would be either 2000 or above since the other part of the equation is +2000.

accessdenied · Answer

yeah, that sounds reasonable.  your book seems to have the error here

anonymous · Answer

Yeah I just wanted to double check, just talked to another student in my class and it appears that this is the consensus. Thanks for your help

anonymous · Answer

0 ≤        C         ≤ 10,000 
0 ≤ 2,000 + 4x  ≤ $10,000 
0 ≤      x            ≤ 2,000  units

accessdenied · Answer

you would also have to carry those operations to the first "0 <=" since it is a compound inequality