Explain equation-solving steps as logical consequences of equality and justify solution methods.
Classify an equation as one solution, no solution, or infinitely many solutions
Problem
Solve and classify \(2(x+3)=2x+6\).
Big Picture
What this problem is really about
The solution count is determined by what remains after both sides are simplified, not by the equation’s original appearance. We’ll expand the grouped side, combine like terms, and compare the resulting expressions. A single variable value, an impossible numerical statement, and an identity have different solution-set meanings, so the terminal statement supplies the classification.
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