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

$y greater than 4 x plus 8$

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

$x$	$y$
$2$	$19$
$4$	$30$
$6$	$41$

$x$	$y$
$2$	$8$
$4$	$16$
$6$	$24$

$x$	$y$
$2$	$13$
$4$	$18$
$6$	$23$

$x$	$y$
$2$	$13$
$4$	$21$
$6$	$29$

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Explanation

Choice A is correct. In each choice, the values of $x$ are $2$ , $4$ , and $6$ . Substituting the first value of $x$ , $2$ , for $x$ in the given inequality yields $y greater than 4 left parenthesis 2 right parenthesis plus 8$ , or $y greater than 16$ . Therefore, when $x equals 2$ , the corresponding value of $y$ must be greater than $16$ . Of the given choices, only choice A is a table where the value of $y$ corresponding to $x equals 2$ is greater than $16$ . To confirm that the other values of $x$ in this table and their corresponding values of $y$ are also solutions to the given inequality, the values of $x$ and $y$ in the table can be substituted for $x$ and $y$ in the given inequality. Substituting $4$ for $x$ and $30$ for $y$ in the given inequality yields $30 greater than 4 left parenthesis 4 right parenthesis plus 8$ , or $30 greater than 24$ , which is true. Substituting $6$ for $x$ and $41$ for $y$ in the given inequality yields $41 greater than 4 left parenthesis 6 right parenthesis plus 8$ , or $41 greater than 32$ , which is true. It follows that for choice A, all the values of $x$ and their corresponding values of $y$ are solutions to the given inequality.

Choice B is incorrect. Substituting $2$ for $x$ and $8$ for $y$ in the given inequality yields $8 greater than 4 left parenthesis 2 right parenthesis plus 8$ , or $8 greater than 16$ , which is false.

Choice C is incorrect. Substituting $2$ for $x$ and $13$ for $y$ in the given inequality yields $13 greater than 4 left parenthesis 2 right parenthesis plus 8$ , or $13 greater than 16$ , which is false.

Choice D is incorrect. Substituting $2$ for $x$ and $13$ for $y$ in the given inequality yields $13 greater than 4 left parenthesis 2 right parenthesis plus 8$ , or $13 greater than 16$ , which is false.