OG详解-OG4 数学2 Q17

Choice B is correct. A linear equation in one variable has no solution if and only if the equation is false; that is, when there is no value of x that produces a truestatement. It’s given that in the equation -3x +21px = 84, p is a constant and the equation has no solution for x. Therefore, the value of the constant p is one that results in a false equation. Factoring out the common factor of -3x on the left-hand side of the given equation yields  -3x(1-7p)= 84. Dividing both sides of this equation by -3 yields x(1-7p)=-28. Dividing both sides of this equation by (1-7p) yields x = −281−7p​​. This equation is false if and only if 1-7p = 0. Adding 7p to both sides of 1-7p = 0 yields 1= 7p. Dividing both sides of this equation by 7 yields1​7​= p. It follows that the equation x = −281−7p​ is false if and only if  p = 1​7​.Therefore, the given equation has no solution if and only if the value of p is 1​7​.
Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.