OG详解-OG10 数学2 Q22

Choice D is correct. By the definition of absolute value, if |-5x+ 13| = 73, then -5x+ 13 = 73 or -5x+13=-73. Subtracting 13 from both sides of the equation -5x+ 13 = 73 yields -5x = 60. Dividing both sides of this equation by -5 yields x =-12. Subtracting 13 from both sides of the equation -5x+ 13 = -73 yields -5x = -86. Dividing both sides of this equation by -5 yields x =865​​. Therefore, the solutions to the given equation are -12 and 865​​ , and it follows that the sum of the solutions to the given equation is -12 + 865​​ , or 2​65​.
Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect. This is a solution, not the sum of the solutions, to the given equation. Choice C is incorrect and may result from conceptual or calculation errors.