Translate verbal phrases and short contexts into algebraic expressions.
Judge whether an expression matches a phrase
Problem
A student translates “\(\text{twice}\) the sum of \(x\) and \(3\)” as \(2(x~+~3)\). Evaluate the translation, and report whether it is valid or invalid followed by the structure-preserving expression.
Big Picture
What this problem is really about
Start with the named sum, which makes x plus three one grouped quantity. The word “twice” must apply to that whole group, so parentheses are the key structural evidence when judging the student’s translation. Distributing mentally checks whether both terms would be doubled and supports the validity decision.
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