Question

the value of a duplicating machine after \\(x\\) copies have been made is given by \\(v = 30,000 - 0.04x\\).

after a few years, an appraiser states that the value of the machine is between \\$15,000 and \\$20,000, which can be represented by the following inequality:

\\15,000 \le 30,000 - 0.04x \le 20,000\\

which of the following inequalities represents the range of the number of copies that were made?

a.) \\(375,000 \le x \le 500,000\\)

b.) \\(345,000 \le x \le 470,000\\)

c.) \\(250,000 \le x \le 375,000\\)

d.) \\(25,000 \le x \le 37,500\\)

Explanation:

Subtract constant from all parts

Using the Linear Inequalities knowledge point

$$
LATEXBLOCK0
$$

Divide by negative coefficient

Using the Inequality Sign Reversal knowledge point

$$
LATEXBLOCK1
$$

Answer:

• a.) \(375,000 \le x \le 500,000\)
• b.) \(345,000 \le x \le 470,000\)
• c.) \(250,000 \le x \le 375,000\) (Correct answer)
• d.) \(25,000 \le x \le 37,500\)