Explain equation-solving steps as logical consequences of equality and justify solution methods.
Complete an equality-preserving solution chain
Problem
Solve \(4(x-3)+5=21\).
Big Picture
What this problem is really about
A correct endpoint is not enough; every arrow in the solution chain must preserve equality. We’ll first rewrite the grouped expression and combine its constants, then use the same inverse operation on both sides to remove the remaining constant and coefficient. Finally, substitution into the untouched original equation will verify the entire chain rather than just its last line.
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