y < 6 x + 2 For which of the following tables are all the values of x and their

Question

y &#60; 6 x + 2 For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?

Accepted Answer

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 < 6 3 + 2 , or y < 20 . Therefore, when x = 3 , the corresponding value of y is less than 20 . Substituting 5 for x in the given inequality yields y < 6 5 + 2 , or y < 32 . Therefore, when x = 5 , the corresponding value of y is less than 32 . Substituting 7 for x in the given inequality yields y < 6 7 + 2 , or y < 44 . Therefore, when x = 7 , the corresponding value of y is less than 44 . For the table in choice C, when x = 3 , the corresponding value of y is 16 , which is less than 20 ; when x = 5 , the corresponding value of y is 28 , which is less than 32 ; when x = 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 = 3 , the corresponding value of y is 20 , which is not less than 20 ; when x = 5 , the corresponding value of y is 32 , which is not less than 32 ; when x = 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 = 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 = 3 , the corresponding value of y is 24 , which is not less than 20 ; when x = 5 , the corresponding value of y is 36 , which is not less than 32 ; when x = 7 , the corresponding value of y is 48 , which is not less than 44 .

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

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

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

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

Question y-60-6