We will solve the equation \(2 (x + 8) = 2x + 8\) step by step, justifying each step.
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Distribute on the left side: \[ 2 (x + 8) = 2x + 16 \] This is done using the distributive property, which states that \(a(b + c) = ab + ac\).
Thus, we rewrite the equation: \[ 2x + 16 = 2x + 8 \]
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Subtract \(2x\) from both sides: \[ 2x + 16 - 2x = 2x + 8 - 2x \] Simplifying both sides yields: \[ 16 = 8 \]
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Evaluate the result: The equation \(16 = 8\) is a false statement. This implies that there are no values of \(x\) that will satisfy the original equation.
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Conclusion: Since we arrived at a contradiction, we conclude that the equation \(2 (x + 8) = 2x + 8\) has no solution.
Thus, the final answer is that the equation has no solution.