Solve linear equations with variables on both sides and interpret special cases.
Write and solve a both-sides equation from a representation
Problem
A level balance has \(2~\text{identical}~\text{boxes}\) of value \(x\) plus \(3~\text{unit}~\text{weights}\) on the left and \(\text{one}~\text{identical}~\text{box}\) plus \(8~\text{unit}~\text{weights}\) on the right. Write the represented equation and solve for \(x\).
The balanced scale turns each tray into a complete expression: two mystery boxes plus three units on one side, and one box plus eight units on the other. Set those expressions equal because the beam is level. Then remove matching quantities from both sides before undoing the remaining constant; every move preserves the balance and exposes one box’s value.
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