Solve linear equations with variables on both sides and interpret special cases.
Solve a fixed both-sides comparison model
Problem
\(\text{Two}~\text{plans}\) have costs \(10~+~2x\) and \(1~+~5x\). Complete the fixed comparison and solve: \(10~+~2x~=~1~+~5x\); \(x~=~\text{\_\_\_}\).
Big Picture
What this problem is really about
The comparison needs an equals sign because both expressions describe costs at the same month. Keep each plan's fixed amount and monthly rate together, then move variable terms to one side and constants to the other. Interpret the solved variable in months and verify that both cost rules give the same total.
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