sat suite question viewer
In the given equation, is a constant. The equation has no solution. What is the value of ?
Explanation
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 that produces a true statement. It's given that in the equation , is a constant and the equation has no solution for . Therefore, the value of the constant is one that results in a false equation. Factoring out the common factor of on the left-hand side of the given equation yields . Dividing both sides of this equation by yields . Dividing both sides of this equation by yields . This equation is false if and only if . Adding to both sides of yields . Dividing both sides of this equation by yields . It follows that the equation is false if and only if . Therefore, the given equation has no solution if and only if the value of is .
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.