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

$y greater than 13 x minus 18$

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

$x$	$y$
$3$	$21$
$5$	$47$
$8$	$86$

$x$	$y$
$3$	$26$
$5$	$42$
$8$	$86$

$x$	$y$
$3$	$16$
$5$	$42$
$8$	$81$

$x$	$y$
$3$	$26$
$5$	$52$
$8$	$91$

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Explanation

Choice D is correct. All the tables in the choices have the same three values of $x$ , 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 $3$ for $x$ in the given inequality yields $y greater than 13 left parenthesis 3 right parenthesis minus 18$ , or $y greater than 21$ . Therefore, when $x equals 3$ , the corresponding value of $y$ is greater than $21$ . Substituting $5$ for $x$ in the given inequality yields $y greater than 13 left parenthesis 5 right parenthesis minus 18$ , or $y greater than 47$ . Therefore, when $x equals 5$ , the corresponding value of $y$ is greater than $47$ . Substituting $8$ for $x$ in the given inequality yields $y greater than 13 left parenthesis 8 right parenthesis minus 18$ , or $y greater than 86$ . Therefore, when $x equals 8$ , the corresponding value of $y$ is greater than $86$ . For the table in choice D, when $x equals 3$ , the corresponding value of $y$ is $26$ , which is greater than $21$ ; when $x equals 5$ , the corresponding value of $y$ is $52$ , which is greater than $47$ ; when $x equals 8$ , the corresponding value of $y$ is $91$ , which is greater than $86$ . 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. In the table for choice A, when $x equals 3$ , the corresponding value of $y$ is $21$ , which is not greater than $21$ ; when $x equals 5$ , the corresponding value of $y$ is $47$ , which is not greater than $47$ ; when $x equals 8$ , the corresponding value of $y$ is $86$ , which is not greater than $86$ .

Choice B is incorrect. In the table for choice B, when $x equals 5$ , the corresponding value of $y$ is $42$ , which is not greater than $47$ ; when $x equals 8$ , the corresponding value of $y$ is $86$ , which is not greater than $86$ .

Choice C is incorrect. In the table for choice C, when $x equals 3$ , the corresponding value of $y$ is $16$ , which is not greater than $21$ ; when $x equals 5$ , the corresponding value of $y$ is $42$ , which is not greater than $47$ ; when $x equals 8$ , the corresponding value of $y$ is $81$ , which is not greater than $86$ .