To find the correct first step in Callie's solution, let's start with the original equation:
\[ 3x + 6(x - 7) = 4(3x + 6) \]
First, we will simplify both sides of the equation:
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Distributing on the left side: \[ 6(x - 7) = 6x - 42 \] So, the left side becomes: \[ 3x + 6x - 42 \]
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Now, simplifying the left side: \[ 3x + 6x - 42 = 9x - 42 \]
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For the right side, distribute \(4\): \[ 4(3x + 6) = 12x + 24 \]
Now the equation looks like this: \[ 9x - 42 = 12x + 24 \]
Now let's compare this to the provided options to find the matching first step:
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3x + 6x – 7 = 12x + 6
- Incorrect. This does not match our simplification.
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3x + 6x – 13 = 7x + 10
- Incorrect. This does not match our simplification.
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3x + 6x + 42 = 12x + 24
- Incorrect. The left-hand side is incorrect.
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3x + 6x – 42 = 12x + 24
- Correct! This is the equation we obtained after distributing.
Therefore, the correct first step in Callie's solution is:
3x + 6x – 42 = 12x + 24.
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