Final answer:
Option (D) 9 - 5x = 13 is the correct equation that is equivalent to the given equation 13 - 5x = 9, as it represents the original equation correctly after switching the sides of the equal sign.
Step-by-step explanation:
The question asks us to find the correct equation that is equivalent to the given equation 13 - 5x = 9. To find the correct equation, we compare the given equation to each of the provided options and look for one that is mathematically equivalent.
Let's examine each option:
- (A) 5x + 13 = 9: This isn't equivalent because the terms are not in the same order and the sign before 13 is opposite to the original equation.
- (B) 13x - 5 = 9: This is incorrect because the coefficient of x is 13 instead of -5, and the constant term is -5 instead of 13.
- (C) 5 - 13x = 9: This equation has the wrong coefficients and the signs are also incorrect.
- (D) 9 - 5x = 13: By reversing the sides of the equal sign of the original equation, we get 9 = 13 - 5x. This option represents the original equation correctly after switching the sides.
- (E) 13x + 5 = 9: This equation has the wrong coefficients.
- (F) 5x - 13 = 9: This isn't equivalent because, although the terms are correct, they are not in the original order and the equation is not balanced with the given equation.
The correct equation that matches 13 - 5x = 9 is option (D) 9 - 5x = 13.