2 x - y > 883 For which of the following tables are all the values of x and their

Question

2 x - y &#62; 883 For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?

Accepted Answer

Choice D is correct. All the tables in the choices have the same three values of x , 440 , 441 , and 442 , so each of the three values of x can be substituted in the given inequality to compare the corresponding values of y in each of the tables. Substituting 440 for x in the given inequality yields 2 440 - y &#62; 883 , or 880 - y &#62; 883 . Subtracting 880 from both sides of this inequality yields - y &#62; 3 . Dividing both sides of this inequality by - 1 yields y &#60; - 3 . Therefore, when x = 440 , the corresponding value of y must be less than - 3 . Substituting 441 for x in the given inequality yields 2 441 - y &#62; 883 , or 882 - y &#62; 883 . Subtracting 882 from both sides of this inequality yields - y &#62; 1 . Dividing both sides of this inequality by - 1 yields y &#60; - 1 . Therefore, when x = 441 , the corresponding value of y must be less than - 1 . Substituting 442 for x in the given inequality yields 2 442 - y &#62; 883 , or 884 - y &#62; 883 . Subtracting 884 from both sides of this inequality yields - y &#62; - 1 . Dividing both sides of this inequality by - 1 yields y &#60; 1 . Therefore, when x = 442 , the corresponding value of y must be less than 1 . For the table in choice D, when x = 440 , the corresponding value of y is - 4 , which is less than - 3 ; when x = 441 , the corresponding value of y is - 2 , which is less than - 1 ; when x = 442 , the corresponding value of y is 0 , which is less than 1 . Therefore, the table in choice D gives values of x and their corresponding values of y that are all solutions to the given inequality. Choice A is incorrect. When x = 440 , the corresponding value of y in this table is 0 , which isn't less than - 3 . Choice B is incorrect. When x = 440 , the corresponding value of y in this table is 0 , which isn't less than - 3 . Choice C is incorrect. When x = 440 , the corresponding value of y in this table is - 2 , which isn't less than - 3 .

$x$	$y$
$440$	$0$
$441$	$negative 2$
$442$	$negative 4$

$x$	$y$
$440$	$0$
$442$	$negative 2$
$441$	$negative 4$

$x$	$y$
$442$	$0$
$440$	$negative 2$
$441$	$negative 4$

$x$	$y$
$442$	$0$
$441$	$negative 2$
$440$	$negative 4$

Question 2-x-y-