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Algebra Difficulty: Hard

$y less than 5 x plus 6$

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

$x$	$y$
$3$	$17$
$5$	$27$
$7$	$37$

$x$	$y$
$3$	$17$
$5$	$35$
$7$	$37$

$x$	$y$
$3$	$25$
$5$	$35$
$7$	$45$

$x$	$y$
$3$	$21$
$5$	$31$
$7$	$41$

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Explanation

Choice A is correct. Substituting $3$ for $x$ in the given inequality yields $y less than 5 left parenthesis 3 right parenthesis plus 6$ , or $y less than 21$ . Therefore, when $x equals 3$ , the corresponding value of $y$ is less than $21$ . Substituting $5$ for $x$ in the given inequality yields $y less than 5 left parenthesis 5 right parenthesis plus 6$ , or $y less than 31$ . Therefore, when $x equals 5$ , the corresponding value of $y$ is less than $31$ . Substituting $7$ for $x$ in the given inequality yields $y less than 5 left parenthesis 7 right parenthesis plus 6$ , or $y less than 41$ . Therefore, when $x equals 7$ , the corresponding value of $y$ is less than $41$ . For the table in choice A, when $x equals 3$ , the corresponding value of $y$ is $17$ , which is less than $21$ ; when $x equals 5$ , the corresponding value of $y$ is $27$ , which is less than $31$ ; and when $x equals 7$ , the corresponding value of $y$ is $37$ , which is less than $41$ . Therefore, the table in choice A gives values of $x$ and their corresponding values of $y$ that are all solutions to the given inequality.

Choice B is incorrect and may result from conceptual or calculation errors.

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

Choice D is incorrect and may result from conceptual or calculation errors.