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Haley solved the equation 25+3n12=13+7n4n25 + 3n - 12 = 13 + 7n - 4n. Here are her last two steps:\newline13+3n=13+3n13 + 3n = 13 + 3n\newline13=1313 = 13\newlineWhich statement is true about the equation?\newline(A)The solution is n=13n = 13.\newline(B)There is no solution because 13=1313 = 13 is a true equation.\newline(C)There are infinitely many solutions because 13=1313 = 13 is a true equation.\newline(D)The solution is (13,13)(13, 13).

Full solution

Q. Haley solved the equation 25+3n12=13+7n4n25 + 3n - 12 = 13 + 7n - 4n. Here are her last two steps:\newline13+3n=13+3n13 + 3n = 13 + 3n\newline13=1313 = 13\newlineWhich statement is true about the equation?\newline(A)The solution is n=13n = 13.\newline(B)There is no solution because 13=1313 = 13 is a true equation.\newline(C)There are infinitely many solutions because 13=1313 = 13 is a true equation.\newline(D)The solution is (13,13)(13, 13).
  1. Simplify left side: Simplify the left side of the equation: 25+3n12=13+7n4n25 + 3n - 12 = 13 + 7n - 4n. Combine like terms: 2512+3n=13+3n25 - 12 + 3n = 13 + 3n.
  2. Combine like terms: Simplify further: 13+3n=13+3n13 + 3n = 13 + 3n.
  3. Further simplification: Subtract 1313 from both sides: 3n=3n3n = 3n.
  4. Subtract 1313: Subtract 3n3n from both sides: 0=00 = 0.

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