Write and solve a linear equation from a short verbal or contextual situation.
Check whether a word-problem solution makes sense
Problem
A van has \(8~\text{seats}\) and \(3\) are filled. Write and solve an equation for the number of empty seats. A result is reasonable only if it is a whole number from \(0~\text{through}~8\) and satisfies the equation. Report the equation, result, and reasonableness judgment.
Big Picture
What this problem is really about
Model all eight seats as the sum of empty seats and the three filled seats, with x counting only the empty ones. After solving, reasonableness needs two checks: substitution must rebuild the total, and the result must be a whole-number seat count within the van’s capacity. Passing both checks connects the algebra back to the physical situation.
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