Solve multi-step linear equations, including equations requiring simplification first.
Match a context to the right multi-step equation
Problem
\(\text{Two}~\text{bikes}\) each cost \(\$3\) for equipment plus \(\$2~\text{per}~\text{hour}\) for \(x~\text{hours}\), totaling \(\$22\). Which complete response correctly models the situation?
A. \(2(x~+~3)~=~22\) B. \(2(2x~+~3)~=~22\) C. \(2x~+~3~=~22\)
Big Picture
What this problem is really about
Build the cost of one bike before accounting for two bikes. One rental combines a two-dollar hourly charge for x hours with one three-dollar equipment fee, and the outer factor must repeat that entire cost. Then reverse the layers: divide by the bike count, remove the fee, and divide by the hourly rate.
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