Solve linear equations with variables on both sides and interpret special cases.
Match equations to solutions or cases
Problem
Solve or simplify \(\text{every}~\text{equation}\) below far enough to classify its solution set. Report the complete set of labels for equations with \(\text{no}~\text{solution}\).
A. \(4x~+~7~=~4x~-~1\) B. \(6x~-~5~=~2x~+~11\) C. \(3(x~+~2)~=~3x~+~6\) D. \(9~-~2x~=~5~-~2x\) E. \(5x~+~8~=~2x~+~8\)
Big Picture
What this problem is really about
Simplify every equation far enough to see what remains after like variable terms are collected. A remaining variable equation gives one value, a true constant statement works for every value, and a false constant statement works for none. Use that three-way test on every label, because cancellation alone does not determine the solution case.
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