Explain equation-solving steps as logical consequences of equality and justify solution methods.
Test whether one equation step is equivalent
Problem
Audit the step \(3(x-2)=15~\to~3x-6=15\).
Big Picture
What this problem is really about
This audit concerns a local rewrite on one side, so the unchanged right side is not evidence of an imbalance. We’ll multiply the existing outside factor by every term in its group, compare the expanded expression with the next line, and then factor the result back. That reversible expression identity determines whether the equation step preserves every solution.
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