Solve multi-step linear equations, including equations requiring simplification first.
Check which transformed equations stay equivalent
Problem
Starting with \(2(x~+~3)~+~x~=~18\), test \(\text{every}~\text{labeled}~\text{equation}\) below using valid algebraic transformations. Report the complete set of labels for equations equivalent to the original.
A. \(3x~+~6~=~18\) B. \(3x~+~3~=~18\) C. \(x~+~3~+~x~=~18\) D. \(3x~=~12\) E. \(x~=~4\) F. \(6~+~3x~=~18\)
Big Picture
What this problem is really about
Establish a trustworthy chain by distributing through the original group and combining like terms. From there, reordering addends or applying the same inverse operation to both sides preserves the solution set. Reject any form that changes a constant or distributes to only part of the group, then retain every equation in the valid chain.
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