Solve linear equations with variables on both sides and interpret special cases.
Choose a specified both-sides simplification
Problem
For \(2x~+~5~=~x~+~13\), which complete response is correct? Candidate A subtracts \(x\) from \(\text{both}~\text{sides}\), B combines \(2x\) and \(x\) across the equals sign, and C subtracts \(5\) from \(\text{both}~\text{sides}\).
Big Picture
What this problem is really about
The requested first move has a specific job: reduce the variable terms while keeping the equation balanced. Look for an operation applied to both sides that cancels one of the x-terms and leaves a simpler equation. Finish isolating x only after that structure is simplified, then check the result in the original equation.
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