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Devin solved the equation 12+5x−7=13x−4−8x12 + 5x - 7 = 13x - 4 - 8x. Here are his last two steps:\newline5+5x=5x−45 + 5x = 5x - 4\newline5=−45 = -4\newlineWhich statement is true about the equation?\newline(A)The solution is x=−4x = -4.\newline(B)There is no solution because 5=−45 = -4 is a false equation.\newline(C)There are infinitely many solutions because 5=−45 = -4 is a false equation.\newline(D)The solution is (5,−4)(5, -4).

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Full solution

Q. Devin solved the equation 12+5x−7=13x−4−8x12 + 5x - 7 = 13x - 4 - 8x. Here are his last two steps:\newline5+5x=5x−45 + 5x = 5x - 4\newline5=−45 = -4\newlineWhich statement is true about the equation?\newline(A)The solution is x=−4x = -4.\newline(B)There is no solution because 5=−45 = -4 is a false equation.\newline(C)There are infinitely many solutions because 5=−45 = -4 is a false equation.\newline(D)The solution is (5,−4)(5, -4).
  1. Simplify left side: Simplify the left side of the equation: 12+5x−7=5x+512 + 5x - 7 = 5x + 5.
  2. Simplify right side: Simplify the right side of the equation: 13x−4−8x=5x−413x - 4 - 8x = 5x - 4.
  3. Set equal: Set the simplified left side equal to the simplified right side: 5+5x=5x−45 + 5x = 5x - 4.
  4. Subtract to isolate: Subtract 5x5x from both sides to isolate constants: 5=−45 = -4.
  5. Recognize no solution: Recognize that 5=−45 = -4 is a false statement, indicating no solution exists.

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