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If (S(x)=s-13x) and (S(6)-S(15)=117), which conclusion is correct?

Answer and explanation

Correct answer: The given condition is true for every \(s\)

\(S(6)=s-13\times6=s-78\) and \(S(15)=s-13\times15=s-195\). Therefore, \(S(6)-S(15)=(s-78)-(s-195)=117\). The terms containing \(s\) cancel, so the condition is true for every value of \(s\). No particular value such as \(s=117\) or \(s=13\) is required. Exam tip: when subtracting function values, check whether common parameter terms cancel.

Related tags

Linear FunctionsPolynomialsParameter CancellationFunction ValuesAlgebraic SimplificationLinear Growth And DecayIntroduction To PolynomialsMathematics

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