A new car worth \( \$ 30,000 \) is depreciating in value by \( \$ 3,000 \) per year. After how many years will the car's value be \( \$ 6,000 \) ? After \( \square \) years, the car's value will be \( \$ 6,000 \).

To find out after how many years the car's value will be \( \$ 6,000 \), we can set up the following equation based on the information given: 1. The initial value of the car is \( \$ 30,000 \). 2. The car depreciates by \( \$ 3,000 \) per year. 3. We want to find the number of years \( x \) when the car's value will be \( \$ 6,000 \). The value of the car after \( x \) years can be expressed as: \[ \text{Value after } x \text{ years} = 30,000 - 3,000x \] We want this value to equal \( 6,000 \): \[ 30,000 - 3,000x = 6,000 \] Now, we can solve for \( x \): 1. Subtract \( 30,000 \) from both sides: \[ -3,000x = 6,000 - 30,000 \] \[ -3,000x = -24,000 \] 2. Divide both sides by \( -3,000 \): \[ x = \frac{-24,000}{-3,000} = 8 \] Thus, after \( 8 \) years, the car's value will be \( \$ 6,000 \). So, the answer is: After \( \boxed{8} \) years, the car's value will be \( \$ 6,000 \).