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

$y less than 6 x plus 2$

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

$x$	$y$
$3$	$20$
$5$	$32$
$7$	$44$

$x$	$y$
$3$	$16$
$5$	$36$
$7$	$40$

$x$	$y$
$3$	$16$
$5$	$28$
$7$	$40$

$x$	$y$
$3$	$24$
$5$	$36$
$7$	$48$

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Explanation

Choice C 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 $y less than 6 left parenthesis 3 right parenthesis plus 2$ , or $y less than 20$ . Therefore, when $x equals 3$ , the corresponding value of $y$ is less than $20$ . Substituting $5$ for $x$ in the given inequality yields $y less than 6 left parenthesis 5 right parenthesis plus 2$ , or $y less than 32$ . Therefore, when $x equals 5$ , the corresponding value of $y$ is less than $32$ . Substituting $7$ for $x$ in the given inequality yields $y less than 6 left parenthesis 7 right parenthesis plus 2$ , or $y less than 44$ . Therefore, when $x equals 7$ , the corresponding value of $y$ is less than $44$ . For the table in choice C, when $x equals 3$ , the corresponding value of $y$ is $16$ , which is less than $20$ ; when $x equals 5$ , the corresponding value of $y$ is $28$ , which is less than $32$ ; when $x equals 7$ , the corresponding value of $y$ is $40$ , which is less than $44$ . Therefore, the table in choice C 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 $20$ , which is not less than $20$ ; when $x equals 5$ , the corresponding value of $y$ is $32$ , which is not less than $32$ ; when $x equals 7$ , the corresponding value of $y$ is $44$ , which is not less than $44$ .

Choice B is incorrect. In the table for choice B, when $x equals 5$ , the corresponding value of $y$ is $36$ , which is not less than $32$ .

Choice D is incorrect. In the table for choice D, when $x equals 3$ , the corresponding value of $y$ is $24$ , which is not less than $20$ ; when $x equals 5$ , the corresponding value of $y$ is $36$ , which is not less than $32$ ; when $x equals 7$ , the corresponding value of $y$ is $48$ , which is not less than $44$ .