- 3 x + 21 p x = 84 In the given equation, p is a constant. The equation has

Question

- 3 x + 21 p x = 84 In the given equation, p is a constant. The equation has no solution. What is the value of p ?

Accepted Answer

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 true statement. It's given that in the equation - 3 x + 21 p x = 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 - 3 x on the left-hand side of the given equation yields - 3 x 1 - 7 p = 84 . Dividing both sides of this equation by - 3 yields x 1 - 7 p = - 28 . Dividing both sides of this equation by 1 - 7 p yields x = - 28 1 - 7 p . This equation is false if and only if 1 - 7 p = 0 . Adding 7 p to both sides of 1 - 7 p = 0 yields 1 = 7 p . Dividing both sides of this equation by 7 yields 1 7 = p . It follows that the equation x = - 28 1 - 7 p 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.

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