Explain equation-solving steps as logical consequences of equality and justify solution methods.
Decide whether a transformation creates an equivalent equation
Problem
Compare \(x+3=7\) with \(x=4\).
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What this problem is really about
Two equations are equivalent only when their complete solution sets match. We’ll identify the balanced operation connecting these forms, check that applying it forward preserves equality, and then reverse it to recover the starting equation. A transformation that works in both directions without a forbidden operation cannot add or discard solutions.
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