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

$y > 7 x - 4$ $y greater than 7 x minus 4$

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

$x$	$y$
$3$	$13$
$5$	$27$
$8$	$48$

$x$	$y$
$3$	$17$
$5$	$31$
$8$	$52$

$x$	$y$
$3$	$21$
$5$	$27$
$8$	$52$

$x$	$y$
$3$	$21$
$5$	$35$
$8$	$56$

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Explanation

Choice D is correct. A solution $(x, y)$ $(x, y)$ to the given inequality is a value of $x$ $x$ and the corresponding value of $y$ $y$ such that the value of $y$ $y$ is greater than the value of $7 x - 4$ $7 x minus 4$ . All the tables in the choices have the same three values of $x$ $x$ , so each of the three values of $x$ $x$ can be substituted in the given inequality to compare the corresponding values of $y$ $y$ in each of the tables. Substituting $3$ $3$ for $x$ $x$ in the given inequality yields $y > 7 (3) - 4$ $y greater than 7 left parenthesis 3 right parenthesis minus 4$ , or $y > 17$ $y greater than 17$ . Substituting $5$ $5$ for $x$ $x$ in the given inequality yields $y > 7 (5) - 4$ $y greater than 7 left parenthesis 5 right parenthesis minus 4$ , or $y > 31$ $y greater than 31$ . Substituting $8$ $8$ for $x$ $x$ in the given inequality yields $y > 7 (8) - 4$ $y greater than 7 left parenthesis 8 right parenthesis minus 4$ , or $y > 52$ $y greater than 52$ . Therefore, when $x = 3$ $x equals 3$ , $x = 5$ $x equals 5$ , and $x = 8$ $x equals 8$ , the corresponding values of $y$ $y$ must be greater than $17$ $17$ , greater than $31$ $31$ , and greater than $52$ $52$ , respectively. In the table in choice D, when $x = 3$ $x equals 3$ , the corresponding value of $y$ $y$ is $21$ $21$ , which is greater than $17$ $17$ ; when $x = 5$ $x equals 5$ , the corresponding value of $y$ $y$ is $35$ $35$ , which is greater than $31$ $31$ ; when $x = 8$ $x equals 8$ , the corresponding value of $y$ $y$ is $56$ $56$ , which is greater than $52$ $52$ . Of the given choices, only choice D gives values of $x$ $x$ and their corresponding values of $y$ $y$ that are all solutions to the given inequality.

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 C is incorrect and may result from conceptual or calculation errors.