Explain equation-solving steps as logical consequences of equality and justify solution methods.
Justify an algebraic transformation
Problem
Fill in the missing justification for this solution step: \(2(x~+~3)~=~14~\to~2x~+~6~=~14\).
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What this problem is really about
Only the left expression changes while the right side stays fixed, so this is an equivalent rewrite rather than an operation on both sides. We’ll track the outside factor to every term inside the parentheses and simplify the resulting products. The pattern used in that expansion identifies the justification, while equivalence confirms that the equation’s solution set is preserved.
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