Explain equation-solving steps as logical consequences of equality and justify solution methods.
Name the equality property used in a solving step
Problem
In the step from \(x~+~7~=~12\) to \(x~=~5\), identify the property of equality used.
Big Picture
What this problem is really about
An equality property is named for the operation performed between lines, not merely for a symbol visible in the starting equation. We’ll compare the before-and-after forms, reconstruct the same hidden operation on both sides, and see which inverse removes the added amount. That balanced operation tells us the precise property that justifies the step.
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