To find out if any of the equations have the same solution, let's solve each equation step by step.
Equation A: \[ -12 + 3x + 2 = x + 2 \] Combine like terms: \[ 3x - 10 = x + 2 \] Subtract \(x\) from both sides: \[ 3x - x - 10 = 2 \] This simplifies to: \[ 2x - 10 = 2 \] Add 10 to both sides: \[ 2x = 12 \] Divide by 2: \[ x = 6 \]
Equation B: \[ 8 - 3(x - 1) = 2 \] Distribute -3: \[ 8 - 3x + 3 = 2 \] Combine like terms: \[ 11 - 3x = 2 \] Subtract 11 from both sides: \[ -3x = 2 - 11 \] This simplifies to: \[ -3x = -9 \] Divide by -3: \[ x = 3 \]
Equation C: \[ -2 + 4x = 10 \] Add 2 to both sides: \[ 4x = 12 \] Divide by 4: \[ x = 3 \]
Now, summarizing the solutions:
- Equation A has \(x = 6\)
- Equation B has \(x = 3\)
- Equation C has \(x = 3\)
Equations B and C have the same solution, which is \(x = 3\).
Conclusion: Equations B and C have the same answer (3).
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