To solve the equation \( 2(x + 8) = 2x + 8 \), we will follow a systematic approach and justify each step.
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Distribute the left side: We start by applying the distributive property on the left side of the equation. \[ 2(x + 8) = 2 \cdot x + 2 \cdot 8 \] This simplifies to: \[ 2x + 16 \]
So, the equation now looks like this: \[ 2x + 16 = 2x + 8 \]
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Subtract \(2x\) from both sides: To isolate the constants, we can subtract \(2x\) from both sides of the equation. \[ (2x + 16) - 2x = (2x + 8) - 2x \] This simplifies to: \[ 16 = 8 \]
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Evaluate the resulting statement: The statement \(16 = 8\) is a contradiction since 16 does not equal 8. This means that the original equation has no solutions.
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Conclusion: Since we arrive at a false statement, we conclude that there are no values of \(x\) that satisfy the equation \( 2(x + 8) = 2x + 8\).
Thus, the final answer is that the equation has no solutions.