2ax − 15 = 3(x + 5) + 5(x − 1)
In the equation above, a is a constant. If no value of x satisfies the equation, what is the value of a ?

Options

A. 1
B. 2
C. 4
D. 8

Answer

C

Explanation

Applying the distributive property of multiplication to the right-hand side of the given equation gives (3x + 15) + (5x − 5), or 8x + 10. An equation in the form cx + d = rx + s will have no solutions if c = r and d `ne` s. Therefore, it follows that the equation 2ax − 15 = 8x + 10 will have no solutions if 2a = 8, or a = 4.
Choice A is incorrect. If a = 1, then the given equation could be written as 2x − 15 = 8x + 10. Since 2 `ne` 8, this equation has exactly one solution. Choice B is incorrect. If a = 2, then the given equation could be written as 4x − 15 = 8x + 10. Since 4 `ne` 8, this equation has exactly one solution. Choice D is incorrect. If a = 8, then the given equation could be written as 16x − 15 = 8x + 10. Since 16 `ne` 8, this equation has exactly one solution.