sat-dog

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 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 ( - ) = - 28 - = by 1 7p yields x - . This equation is false if and only if 1 7p 0. Adding 1 7p - = = 7p to both sides of 1 7p 0 yields 1 7p. Dividing both sides of this equation - 1= = 28 =1 by 7 yields p. It follows that the equation x - is false if and only if p . 7 1 7p 7 1 Therefore, the given equation has no solution if and only if the value of p is . 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.