Question

the value (\\(v\\), in dollars) of a vehicle depends on the miles (\\(x\\)) that it has been driven, as given by the formula \\(v = 20,000 - 0.4x\\). after one year, the value of the vehicle is between \\$18,000 and \\$19,000, which can be expressed as follows:

\\18,000 \le 20,000 - 0.4x \le 19,000\\

which compound inequality represents the range for the miles driven? answer choices are rounded to the nearest whole number.

\\(4,000 \le x \le 8,000\\)
\\(15,200 \le x \le 15,600\\)
\\(400 \le x \le 800\\)
\\(2,500 \le x \le 5,000\\)

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) \(4,000 \le x \le 8,000\)
• (B) \(15,200 \le x \le 15,600\)
• (C) \(400 \le x \le 800\)
• (D) \(2,500 \le x \le 5,000\) (Correct answer)