\(\text{One}~\text{gym}\)'s pricing rule is \(6v~+~4~\text{dollars}\) and another gym's rule is \(6v~+~11~\text{dollars}\). Set the rules equal to model a matching cost, then classify the equation as having \(\text{one}~\text{solution}\), \(\text{no}~\text{solution}\), or infinitely many solutions. Report the comparison equation and classification.

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6v + 4 = 6v + 11; all real numbers

6v + 4 and 6v + 11; no solution

6(v + 4) = 6(v + 11); no solution

6v + 4 = 6v + 11; no solution

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Curriculum context

Course: Math Foundations
Standard: MF.EQ.8
Category: Pre-Algebra
Domain: Equations
Objective: Solve linear equations with variables on both sides and interpret special cases.
Problem type: Translate a comparison statement into an equation