x - 29 = x - a x - 29 Which of the following are solutions to the given equation,

Question

x - 29 = x - a x - 29 Which of the following are solutions to the given equation, where a is a constant and a &#62; 30 ? a a + 1 29

Accepted Answer

Choice C is correct. Subtracting the expression x - 29 from both sides of the given equation yields 0 = x - a x - 29 - x - 29 , which can be rewritten as 0 = x - a x - 29 + - 1 x - 29 . Since the two terms on the right-hand side of this equation have a common factor of x - 29 , it can be rewritten as 0 = x - 29 x - a + - 1 , or 0 = x - 29 x - a - 1 . Since x - a - 1 is equivalent to x - a + 1 , the equation 0 = x - 29 x - a - 1 can be rewritten as 0 = x - 29 x - a + 1 . By the zero product property, it follows that x - 29 = 0 or x - a + 1 = 0 . Adding 29 to both sides of the equation x - 29 = 0 yields x = 29 . Adding a + 1 to both sides of the equation x - a + 1 = 0 yields x = a + 1 . Therefore, the two solutions to the given equation are 29 and a + 1 . Thus, only a + 1 and 29 , not a , are solutions to the given equation. Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

Question x-29-x