To model the situation described, we start with the initial fee and the cost per mile:
- Initial fee: $4
- Cost per mile: $2
- Total cost: $28
The equation that represents the total cost of the taxi ride can be set up as follows:
\[ 4 + 2x = 28 \]
Where \( x \) is the number of miles traveled.
Now, let's solve the equation:
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Subtract 4 from both sides: \[ 2x = 28 - 4 \] \[ 2x = 24 \]
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Divide both sides by 2: \[ x = \frac{24}{2} \] \[ x = 12 \]
This means the taxi traveled 12 miles.
Looking at the options provided:
- A: \( 2 + 4x = 28; x = 7.5 \) (Incorrect)
- B: \( 4 + 2x = 28; x = 16 \) (Incorrect)
- C: \( 2 + 4x = 28; x = 6.5 \) (Incorrect)
- D: \( 4 + 2x = 28; x = 12 \) (Correct)
Therefore, the correct choice is D:
\[ 4 + 2x = 28; , x = 12 \]