Evaluate algebraic expressions correctly using substitution and order of operations.
Screen a mixed set for correct evaluation work
Problem
Evaluate \(2x~+~1\) for \(x~=~-3\). Test \(\text{every}~\text{labeled}~\text{line}\) below as a substitution step, arithmetic step, or final result, then report the \(\text{complete}~\text{set}~\text{of}~\text{valid}~\text{labels}\).
A. \(2(-3)~+~1\) B. \(-6~+~1\) C. \(2(3)~+~1\) D. \(-5\) E. \(2(-3~+~1)\) F. \(2(-3)~=~-6,~\text{then}~-6~+~1~=~-5\)
Big Picture
What this problem is really about
First establish the correct chain from substitution through the intermediate arithmetic to the final value. Test every labeled line against that chain: a line may be valid at any stage, but it must preserve the negative input, original grouping, and operation order. Report all matching labels, including any complete worked sequence.
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