To collect all variables on one side of the equation for the original equation \( 12(6x + 8) = x - 8 \), we first simplify the left side.
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Distributing \( 12 \) on the left side: \[ 12(6x + 8) = 72x + 96 \] So the equation becomes: \[ 72x + 96 = x - 8 \]
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Now subtract \( x \) from both sides: \[ 72x - x + 96 = -8 \] Which simplifies to: \[ 71x + 96 = -8 \]
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Next, subtract \( 96 \) from both sides: \[ 71x = -8 - 96 \] Which gives: \[ 71x = -104 \]
Now, we can rearrange the equation to have all variables and constants on one side. A few possible equations derived from this might look like:
- \( 71x + 104 = 0 \)
- \( -71x - 104 = 0 \)
- \( 71x = -104 \)
Using your listed responses, let's verify:
- 4 = -2x - 8 → Not correct based on original equation.
- 3x = x - 12 → Not correct based on original simplified equation.
- 8 = -2x - 8 → Not correct based on original equation.
- 2x + 4 = -8 → Not directly relatable.
- 3x + 12 = x → Not correct based on original relation.
- 2x + 8 = 8 → Not directly correct.
The applicable forms I'm seeing in your options are not ideally matching the transition I see from the given initial form after simplification. Please check the possible variable manipulations, as none of these match my transformation exactly.
1 answer