{"id":"cb_question_bank:a04b10a7-dd6a-455d-93a2-1cc9863ed8df","source_id":"cb_question_bank","source_item_id":"a04b10a7-dd6a-455d-93a2-1cc9863ed8df","external_id":"f77e335f-77c7-457b-b90f-ba4526c10c28","ibn":null,"question_id":"48fb34c8","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.E.","skill":"Linear inequalities in one or two variables","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"y greater than 13 x minus 18 For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"y greater than 13 x minus 18\"><mi>y</mi><mo>&gt;</mo><mrow><mn>13</mn></mrow><mi>x</mi><mo>-</mo><mrow><mn>18</mn></mrow></math></p>\n<p style=\"text-align: left;\">For which of the following tables are all the values of <math alttext=\"x\"><mi>x</mi>\n</math> and their corresponding values of <math alttext=\"y\"><mi>y</mi>\n</math> solutions to the given inequality?</p>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. All the tables in the choices have the same three values of <math alttext=\"x\"><mi>x</mi>\n</math>, so each of the three values of <math alttext=\"x\"><mi>x</mi>\n</math> can be substituted in the given inequality to compare the corresponding values of <math alttext=\"y\"><mi>y</mi>\n</math> in each of the tables. Substituting <math alttext=\"3\"><mn>3</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the given inequality yields <math alttext=\"y greater than 13 left parenthesis 3 right parenthesis minus 18\"><mi>y</mi><mo>&gt;</mo><mn>13</mn><mfenced><mn>3</mn></mfenced><mo>-</mo><mn>18</mn></math>, or <math alttext=\"y greater than 21\"><mi>y</mi><mo>&gt;</mo><mn>21</mn></math>. Therefore, when <math alttext=\"x equals 3\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>3</mn>\n</mrow>\n</math>, the corresponding value of <math alttext=\"y\"><mi>y</mi>\n</math> is greater than <math alttext=\"21\"><mn>21</mn>\n</math>. Substituting <math alttext=\"5\"><mn>5</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the given inequality yields <math alttext=\"y greater than 13 left parenthesis 5 right parenthesis minus 18\"><mi>y</mi><mo>&gt;</mo><mn>13</mn><mfenced><mn>5</mn></mfenced><mo>-</mo><mn>18</mn></math>, or <math alttext=\"y greater than 47\"><mi>y</mi><mo>&gt;</mo><mn>47</mn></math>. Therefore, when <math alttext=\"x equals 5\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>5</mn>\n</mrow>\n</math>, the corresponding value of <math alttext=\"y\"><mi>y</mi>\n</math> is greater than <math alttext=\"47\"><mn>47</mn>\n</math>. Substituting <math alttext=\"8\"><mn>8</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the given inequality yields <math alttext=\"y greater than 13 left parenthesis 8 right parenthesis minus 18\"><mi>y</mi><mo>&gt;</mo><mn>13</mn><mfenced><mn>8</mn></mfenced><mo>-</mo><mn>18</mn></math>, or <math alttext=\"y greater than 86\"><mi>y</mi><mo>&gt;</mo><mn>86</mn></math>. Therefore, when <math alttext=\"x equals 8\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>8</mn>\n</mrow>\n</math>, the corresponding value of <math alttext=\"y\"><mi>y</mi>\n</math> is greater than <math alttext=\"86\"><mn>86</mn>\n</math>. For the table in choice D, when <math alttext=\"x equals 3\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>3</mn>\n</mrow>\n</math>, the corresponding value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"26\"><mn>26</mn>\n</math>, which is greater than <math alttext=\"21\"><mn>21</mn>\n</math>; when <math alttext=\"x equals 5\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>5</mn>\n</mrow>\n</math>, the corresponding value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"52\"><mn>52</mn>\n</math>, which is greater than <math alttext=\"47\"><mn>47</mn>\n</math>; when <math alttext=\"x equals 8\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>8</mn>\n</mrow>\n</math>, the corresponding value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"91\"><mn>91</mn>\n</math>, which is greater than <math alttext=\"86\"><mn>86</mn>\n</math>. Therefore, the table in choice D gives values of <math alttext=\"x\"><mi>x</mi>\n</math> and their corresponding values of <math alttext=\"y\"><mi>y</mi>\n</math> that are all solutions to the given inequality.</p>\n<p style=\"text-align: left;\">Choice A is incorrect. In the table for choice A, when <math alttext=\"x equals 3\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>3</mn>\n</mrow>\n</math>, the corresponding value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"21\"><mn>21</mn>\n</math>, which is not greater than <math alttext=\"21\"><mn>21</mn>\n</math>; when <math alttext=\"x equals 5\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>5</mn>\n</mrow>\n</math>, the corresponding value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"47\"><mn>47</mn>\n</math>, which is not greater than <math alttext=\"47\"><mn>47</mn>\n</math>; when <math alttext=\"x equals 8\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>8</mn>\n</mrow>\n</math>, the corresponding value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"86\"><mn>86</mn>\n</math>, which is not greater than <math alttext=\"86\"><mn>86</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. In the table for choice B, when <math alttext=\"x equals 5\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>5</mn>\n</mrow>\n</math>, the corresponding value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"42\"><mn>42</mn>\n</math>, which is not greater than <math alttext=\"47\"><mn>47</mn>\n</math>; when <math alttext=\"x equals 8\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>8</mn>\n</mrow>\n</math>, the corresponding value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"86\"><mn>86</mn>\n</math>, which is not greater than <math alttext=\"86\"><mn>86</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. In the table for choice C, when <math alttext=\"x equals 3\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>3</mn>\n</mrow>\n</math>, the corresponding value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"16\"><mn>16</mn>\n</math>, which is not greater than <math alttext=\"21\"><mn>21</mn>\n</math>; when <math alttext=\"x equals 5\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>5</mn>\n</mrow>\n</math>, the corresponding value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"42\"><mn>42</mn>\n</math>, which is not greater than <math alttext=\"47\"><mn>47</mn>\n</math>; when <math alttext=\"x equals 8\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>8</mn>\n</mrow>\n</math>, the corresponding value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"81\"><mn>81</mn>\n</math>, which is not greater than <math alttext=\"86\"><mn>86</mn>\n</math>.</p>","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":true,"source_created_at":"2023-08-02T20:25:59.820000+00:00","source_updated_at":"2023-08-02T20:25:59.820000+00:00","options":[{"label":"A","content_html":"<figure class=\"table left-justified\"><figure class=\"table left-justified\"><figure class=\"table left-justified\"><figure class=\"table left-justified\"><table border=\"1\">\n<tbody>\n<tr>\n<th style=\"text-align: center;    width: 34.6701px;\" scope=\"col\" id=\"2a690a95-add1-493c-866c-37244b973c72_option_1_tableColumn_1\"><math alttext=\"x\"><mi>x</mi>\n</math></th>\n<th style=\"text-align: center;    width: 41.8403px;\" scope=\"col\" id=\"2a690a95-add1-493c-866c-37244b973c72_option_1_tableColumn_2\"><math alttext=\"y\"><mi>y</mi>\n</math></th>\n</tr>\n<tr>\n<td style=\" text-align: center;\"><math alttext=\"3\"><mn>3</mn>\n</math></td>\n<td style=\" text-align: center;\"><math alttext=\"21\"><mn>21</mn>\n</math></td>\n</tr>\n<tr>\n<td style=\" text-align: center;\"><math alttext=\"5\"><mn>5</mn>\n</math></td>\n<td style=\" text-align: center;\"><math alttext=\"47\"><mn>47</mn>\n</math></td>\n</tr>\n<tr>\n<td style=\" text-align: center;\"><math alttext=\"8\"><mn>8</mn>\n</math></td>\n<td style=\" text-align: center;\"><math alttext=\"86\"><mn>86</mn>\n</math></td>\n</tr>\n</tbody>\n</table></figure></figure></figure></figure>","ord":0},{"label":"B","content_html":"<figure class=\"table left-justified\"><figure class=\"table left-justified\"><figure class=\"table left-justified\"><figure class=\"table left-justified\"><table border=\"1\">\n<tbody>\n<tr>\n<th style=\"text-align: center;    width: 34.6701px;\" scope=\"col\" id=\"20f2f5d8-dbab-4241-a10e-29e9f9f72fc1_option_2_tableColumn_1\"><math alttext=\"x\"><mi>x</mi>\n</math></th>\n<th style=\"text-align: center;    width: 41.8403px;\" scope=\"col\" id=\"20f2f5d8-dbab-4241-a10e-29e9f9f72fc1_option_2_tableColumn_2\"><math alttext=\"y\"><mi>y</mi>\n</math></th>\n</tr>\n<tr>\n<td style=\" text-align: center;\"><math alttext=\"3\"><mn>3</mn>\n</math></td>\n<td style=\" text-align: center;\"><math alttext=\"26\"><mn>26</mn>\n</math></td>\n</tr>\n<tr>\n<td style=\" text-align: center;\"><math alttext=\"5\"><mn>5</mn>\n</math></td>\n<td style=\" text-align: center;\"><math alttext=\"42\"><mn>42</mn>\n</math></td>\n</tr>\n<tr>\n<td style=\" text-align: center;\"><math alttext=\"8\"><mn>8</mn>\n</math></td>\n<td style=\" text-align: center;\"><math alttext=\"86\"><mn>86</mn>\n</math></td>\n</tr>\n</tbody>\n</table></figure></figure></figure></figure>","ord":1},{"label":"C","content_html":"<figure class=\"table left-justified\"><figure class=\"table left-justified\"><figure class=\"table left-justified\"><figure class=\"table left-justified\"><table border=\"1\">\n<tbody>\n<tr style=\"height: 12.3984px;\">\n<th style=\"text-align: center;    width: 34.6701px;\" scope=\"col\" id=\"c21dcdab-fa4e-4605-8e0b-19cd99fa82dc_option_3_tableColumn_1\"><math alttext=\"x\"><mi>x</mi>\n</math></th>\n<th style=\"text-align: center;    width: 41.8403px;\" scope=\"col\" id=\"c21dcdab-fa4e-4605-8e0b-19cd99fa82dc_option_3_tableColumn_2\"><math alttext=\"y\"><mi>y</mi>\n</math></th>\n</tr>\n<tr style=\"height: 22.3984px;\">\n<td style=\"\"><math alttext=\"3\"><mn>3</mn>\n</math></td>\n<td style=\"\"><math alttext=\"16\"><mn>16</mn>\n</math></td>\n</tr>\n<tr style=\"height: 22.3984px;\">\n<td style=\"\"><math alttext=\"5\"><mn>5</mn>\n</math></td>\n<td style=\"\"><math alttext=\"42\"><mn>42</mn>\n</math></td>\n</tr>\n<tr style=\"height: 22.3984px;\">\n<td style=\"\"><math alttext=\"8\"><mn>8</mn>\n</math></td>\n<td style=\"\"><math alttext=\"81\"><mn>81</mn>\n</math></td>\n</tr>\n</tbody>\n</table></figure></figure></figure></figure>","ord":2},{"label":"D","content_html":"<figure class=\"table left-justified\"><figure class=\"table left-justified\"><figure class=\"table left-justified\"><figure class=\"table left-justified\"><table border=\"1\">\n<thead>\n<tr style=\"height: 22.3984px;\">\n<th style=\"\" scope=\"col\"><math alttext=\"x\"><mi>x</mi>\n</math></th>\n<th style=\"\" scope=\"col\"><math alttext=\"y\"><mi>y</mi>\n</math></th>\n</tr>\n</thead>\n<tbody>\n<tr style=\"height: 22.3984px;\">\n<td style=\"width: 34.6701px;\" id=\"5182f7b4-05dc-42ab-911f-0c8fd6dd829d_option_4_tableColumn_1\"><math alttext=\"3\"><mn>3</mn>\n</math></td>\n<td style=\"width: 41.8403px;\" id=\"5182f7b4-05dc-42ab-911f-0c8fd6dd829d_option_4_tableColumn_2\"><math alttext=\"26\"><mn>26</mn>\n</math></td>\n</tr>\n<tr style=\"height: 22.3984px;\">\n<td style=\"\"><math alttext=\"5\"><mn>5</mn>\n</math></td>\n<td style=\"\"><math alttext=\"52\"><mn>52</mn>\n</math></td>\n</tr>\n<tr style=\"height: 22.3984px;\">\n<td style=\"\"><math alttext=\"8\"><mn>8</mn>\n</math></td>\n<td style=\"\"><math alttext=\"91\"><mn>91</mn>\n</math></td>\n</tr>\n</tbody>\n</table></figure></figure></figure></figure>","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}