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Algebra / Linear inequalities in one or two variables Difficulty: Medium

$2 x minus y greater than 883$

For which of the following tables are all the values of $x$ and their corresponding values of $y$ solutions to the given inequality?

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

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

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

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

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Explanation

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 $2 left parenthesis 440 right parenthesis minus y greater than 883$ , or $880 minus y greater than 883$ . Subtracting $880$ from both sides of this inequality yields $negative y greater than 3$ . Dividing both sides of this inequality by $negative 1$ yields $y less than negative 3$ . Therefore, when $x equals 440$ , the corresponding value of $y$ must be less than $negative 3$ . Substituting $441$ for $x$ in the given inequality yields $2 left parenthesis 441 right parenthesis minus y greater than 883$ , or $882 minus y greater than 883$ . Subtracting $882$ from both sides of this inequality yields $negative y greater than 1$ . Dividing both sides of this inequality by $negative 1$ yields $y less than negative 1$ . Therefore, when $x equals 441$ , the corresponding value of $y$ must be less than $negative 1$ . Substituting $442$ for $x$ in the given inequality yields $2 left parenthesis 442 right parenthesis minus y greater than 883$ , or $884 minus y greater than 883$ . Subtracting $884$ from both sides of this inequality yields $- y > - 1$ . Dividing both sides of this inequality by $negative 1$ yields $y less than 1$ . Therefore, when $x equals 442$ , the corresponding value of $y$ must be less than $1$ . For the table in choice D, when $x equals 440$ , the corresponding value of $y$ is $negative 4$ , which is less than $negative 3$ ; when $x equals 441$ , the corresponding value of $y$ is $negative 2$ , which is less than $negative 1$ ; when $x equals 442$ , 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 $x equals 440$ , the corresponding value of $y$ in this table is $0$ , which isn't less than $negative 3$ .

Choice B is incorrect. When $x equals 440$ , the corresponding value of $y$ in this table is $0$ , which isn't less than $negative 3$ .

Choice C is incorrect. When $x equals 440$ , the corresponding value of $y$ in this table is $negative 2$ , which isn't less than $negative 3$ .