{"id":1711,"date":"2016-06-24T23:30:10","date_gmt":"2016-06-24T23:30:10","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/?post_type=chapter&#038;p=1711"},"modified":"2018-12-25T19:49:24","modified_gmt":"2018-12-25T19:49:24","slug":"why-it-matters-linear-inequalities","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/chapter\/why-it-matters-linear-inequalities\/","title":{"raw":"Why It Matters: Linear Inequalities","rendered":"Why It Matters: Linear Inequalities"},"content":{"raw":"<h2>Why Learn about Linear Inequalities?<\/h2>\r\nPreviously, we introduced\u00a0Widmark's formula\u00a0for calculating blood alcohol content:\r\n<p style=\"text-align: center\">[latex]\\text{B} = -0.015t +\\left(\\dfrac{2.84N}{Wg}\\normalsize\\right)[\/latex]<\/p>\r\n<p style=\"text-align: left\">where<\/p>\r\n\r\n<ul>\r\n \t<li style=\"text-align: left\">B = percentage of BAC<\/li>\r\n \t<li style=\"text-align: left\">t = number of hours since the first drink<\/li>\r\n \t<li style=\"text-align: left\">N = number of \u201cstandard drinks\u201d (a standard drink is one\u00a0[latex]12[\/latex]-ounce beer, one [latex]5[\/latex]-ounce glass of wine, or one [latex]1.5[\/latex]-ounce shot of liquor). N should be at least\u00a0[latex]1[\/latex].<\/li>\r\n \t<li style=\"text-align: left\">W = weight in pounds<\/li>\r\n \t<li style=\"text-align: left\">g = gender constant: [latex]0.68[\/latex] for men and\u00a0[latex]0.55[\/latex] for women<\/li>\r\n<\/ul>\r\n<p style=\"text-align: left\">Remember Joan? When we left her, she was at a party. She had three drinks and then wanted to leave. This was worrisome. We posed the following questions:<\/p>\r\n\r\n<ol>\r\n \t<li style=\"text-align: left\">Where would she fall on the table of the progressive effects of alcohol after\u00a0[latex]1.5[\/latex] hours?<\/li>\r\n \t<li style=\"text-align: left\">Would she be within the legal limit to drive after this amount of time?<\/li>\r\n<\/ol>\r\nWe found that Joan's BAC was\u00a0[latex]0.092\\%[\/latex] and by using the table below, she's probably experiencing blunted feelings, reduced sensitivity to pain, euphoria, disinhibition, and extroversion. In addition, her reasoning, depth perception, peripheral vision, and glare recovery are probably\u00a0impaired.\r\n\r\nAdditionally, we determined that she would not be within the legal limit to drive assuming the legal limit is\u00a0[latex]0.08\\%[\/latex]. \u00a0Joan needs a ride home, or she needs to wait until she has metabolized the alcohol in her system so she can safely drive.\r\n\r\nNow we will pose another question that may help her plan\u00a0how long she needs to wait before she drives after drinking at a party.\r\n<ol>\r\n \t<li style=\"text-align: left\">Given any amount that she drinks, can you figure out how much time should pass before she can drive safely and legally?<\/li>\r\n<\/ol>\r\nWe solved for BAC given three standard drinks,\u00a0[latex]1.5[\/latex] hours, and Joan's weight. What is different about this question? What are we solving, an equation or an inequality?\r\n\r\nAfter working through the readings, videos and problems sets in this module, you will hopefully realize that you can answer this question with an inequality. We will revisit the answer to this question at the end of the module.\r\n\r\nIn the following table, the progressive effects of alcohol are defined for ranges of blood alcohol content.\r\n<table class=\"wikitable\">\r\n<tbody>\r\n<tr>\r\n<th style=\"text-align: center\" colspan=\"3\">Progressive effects of alcohol<\/th>\r\n<\/tr>\r\n<tr>\r\n<th>BAC (% by vol.)<\/th>\r\n<th>Behavior<\/th>\r\n<th>Impairment<\/th>\r\n<\/tr>\r\n<tr>\r\n<td align=\"center\">[latex]0.001\u20130.029[\/latex]<\/td>\r\n<td>\r\n<ul>\r\n \t<li>Average individual appears normal<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul>\r\n \t<li>Subtle effects that can be detected with special tests<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td align=\"center\">[latex]0.030\u20130.059[\/latex]<\/td>\r\n<td>\r\n<ul>\r\n \t<li>Mild euphoria<\/li>\r\n \t<li>Relaxation<\/li>\r\n \t<li>Joyousness<\/li>\r\n \t<li>Talkativeness<\/li>\r\n \t<li>Decreased inhibition<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul>\r\n \t<li>Concentration<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td align=\"center\">[latex]0.060\u20130.099[\/latex]<\/td>\r\n<td>\r\n<ul>\r\n \t<li>Blunted feelings<\/li>\r\n \t<li>Reduced sensitivity to pain<\/li>\r\n \t<li>Euphoria<\/li>\r\n \t<li>Disinhibition<\/li>\r\n \t<li>Extroversion<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul>\r\n \t<li>Reasoning<\/li>\r\n \t<li>Depth perception<\/li>\r\n \t<li>Peripheral vision<\/li>\r\n \t<li>Glare recovery<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td align=\"center\">[latex]0.100\u20130.199[\/latex]<\/td>\r\n<td>\r\n<ul>\r\n \t<li>Overexpression<\/li>\r\n \t<li>Boisterousness<\/li>\r\n \t<li>Possibility of nausea and vomiting<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul>\r\n \t<li>Reflexes<\/li>\r\n \t<li>Reaction time<\/li>\r\n \t<li>Gross motor control<\/li>\r\n \t<li>Staggering<\/li>\r\n \t<li>Slurred speech<\/li>\r\n \t<li>Temporary erectile dysfunction<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td align=\"center\">[latex]0.200\u20130.299[\/latex]<\/td>\r\n<td>\r\n<ul>\r\n \t<li>Nausea<\/li>\r\n \t<li>Vomiting<\/li>\r\n \t<li>Emotional swings<\/li>\r\n \t<li>Anger or sadness<\/li>\r\n \t<li>Partial loss of understanding<\/li>\r\n \t<li>Impaired sensations<\/li>\r\n \t<li>Decreased libido<\/li>\r\n \t<li>Possibility of stupor<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul>\r\n \t<li>Severe motor impairment<\/li>\r\n \t<li>Loss of consciousness<\/li>\r\n \t<li>Memory blackout<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td align=\"center\">[latex]0.300\u20130.399[\/latex]<\/td>\r\n<td>\r\n<ul>\r\n \t<li>Stupor<\/li>\r\n \t<li>Central nervous system depression<\/li>\r\n \t<li>Loss of understanding<\/li>\r\n \t<li>Lapses in and out of consciousness<\/li>\r\n \t<li>Low possibility of death<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul>\r\n \t<li>Bladder function<\/li>\r\n \t<li>Breathing<\/li>\r\n \t<li>Dysequilibrium<\/li>\r\n \t<li>Heart rate<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td align=\"center\">[latex]0.400\u20130.500[\/latex]<\/td>\r\n<td>\r\n<ul>\r\n \t<li>Severe central nervous system depression<\/li>\r\n \t<li>Coma<\/li>\r\n \t<li>Possibility of death<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul>\r\n \t<li>Breathing<\/li>\r\n \t<li>Heart rate<\/li>\r\n \t<li>Positional Alcohol Nystagmus<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td align=\"center\">[latex]&gt;0.50[\/latex]<\/td>\r\n<td>\r\n<ul>\r\n \t<li>High risk of poisoning<\/li>\r\n \t<li>High possibility of death<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul>\r\n \t<li>Life<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nJoan likes to party and believes she is \"just fine\" when it comes to driving. At a\u00a0party, though, she downs\u00a0three standard drinks, one after the other, and then decides to leave. If Joan weighs [latex]135[\/latex] pounds, where would she be\u00a0on the table of the progressive effects of alcohol after\u00a0[latex]1.5[\/latex] hours? Would she be within the legal limit to drive home after this amount of time? Given any amount that she drinks, can you figure out how long she must wait\u00a0before she can drive safely and legally?","rendered":"<h2>Why Learn about Linear Inequalities?<\/h2>\n<p>Previously, we introduced\u00a0Widmark&#8217;s formula\u00a0for calculating blood alcohol content:<\/p>\n<p style=\"text-align: center\">[latex]\\text{B} = -0.015t +\\left(\\dfrac{2.84N}{Wg}\\normalsize\\right)[\/latex]<\/p>\n<p style=\"text-align: left\">where<\/p>\n<ul>\n<li style=\"text-align: left\">B = percentage of BAC<\/li>\n<li style=\"text-align: left\">t = number of hours since the first drink<\/li>\n<li style=\"text-align: left\">N = number of \u201cstandard drinks\u201d (a standard drink is one\u00a0[latex]12[\/latex]-ounce beer, one [latex]5[\/latex]-ounce glass of wine, or one [latex]1.5[\/latex]-ounce shot of liquor). N should be at least\u00a0[latex]1[\/latex].<\/li>\n<li style=\"text-align: left\">W = weight in pounds<\/li>\n<li style=\"text-align: left\">g = gender constant: [latex]0.68[\/latex] for men and\u00a0[latex]0.55[\/latex] for women<\/li>\n<\/ul>\n<p style=\"text-align: left\">Remember Joan? When we left her, she was at a party. She had three drinks and then wanted to leave. This was worrisome. We posed the following questions:<\/p>\n<ol>\n<li style=\"text-align: left\">Where would she fall on the table of the progressive effects of alcohol after\u00a0[latex]1.5[\/latex] hours?<\/li>\n<li style=\"text-align: left\">Would she be within the legal limit to drive after this amount of time?<\/li>\n<\/ol>\n<p>We found that Joan&#8217;s BAC was\u00a0[latex]0.092\\%[\/latex] and by using the table below, she&#8217;s probably experiencing blunted feelings, reduced sensitivity to pain, euphoria, disinhibition, and extroversion. In addition, her reasoning, depth perception, peripheral vision, and glare recovery are probably\u00a0impaired.<\/p>\n<p>Additionally, we determined that she would not be within the legal limit to drive assuming the legal limit is\u00a0[latex]0.08\\%[\/latex]. \u00a0Joan needs a ride home, or she needs to wait until she has metabolized the alcohol in her system so she can safely drive.<\/p>\n<p>Now we will pose another question that may help her plan\u00a0how long she needs to wait before she drives after drinking at a party.<\/p>\n<ol>\n<li style=\"text-align: left\">Given any amount that she drinks, can you figure out how much time should pass before she can drive safely and legally?<\/li>\n<\/ol>\n<p>We solved for BAC given three standard drinks,\u00a0[latex]1.5[\/latex] hours, and Joan&#8217;s weight. What is different about this question? What are we solving, an equation or an inequality?<\/p>\n<p>After working through the readings, videos and problems sets in this module, you will hopefully realize that you can answer this question with an inequality. We will revisit the answer to this question at the end of the module.<\/p>\n<p>In the following table, the progressive effects of alcohol are defined for ranges of blood alcohol content.<\/p>\n<table class=\"wikitable\">\n<tbody>\n<tr>\n<th style=\"text-align: center\" colspan=\"3\">Progressive effects of alcohol<\/th>\n<\/tr>\n<tr>\n<th>BAC (% by vol.)<\/th>\n<th>Behavior<\/th>\n<th>Impairment<\/th>\n<\/tr>\n<tr>\n<td align=\"center\">[latex]0.001\u20130.029[\/latex]<\/td>\n<td>\n<ul>\n<li>Average individual appears normal<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul>\n<li>Subtle effects that can be detected with special tests<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\">[latex]0.030\u20130.059[\/latex]<\/td>\n<td>\n<ul>\n<li>Mild euphoria<\/li>\n<li>Relaxation<\/li>\n<li>Joyousness<\/li>\n<li>Talkativeness<\/li>\n<li>Decreased inhibition<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul>\n<li>Concentration<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\">[latex]0.060\u20130.099[\/latex]<\/td>\n<td>\n<ul>\n<li>Blunted feelings<\/li>\n<li>Reduced sensitivity to pain<\/li>\n<li>Euphoria<\/li>\n<li>Disinhibition<\/li>\n<li>Extroversion<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul>\n<li>Reasoning<\/li>\n<li>Depth perception<\/li>\n<li>Peripheral vision<\/li>\n<li>Glare recovery<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\">[latex]0.100\u20130.199[\/latex]<\/td>\n<td>\n<ul>\n<li>Overexpression<\/li>\n<li>Boisterousness<\/li>\n<li>Possibility of nausea and vomiting<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul>\n<li>Reflexes<\/li>\n<li>Reaction time<\/li>\n<li>Gross motor control<\/li>\n<li>Staggering<\/li>\n<li>Slurred speech<\/li>\n<li>Temporary erectile dysfunction<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\">[latex]0.200\u20130.299[\/latex]<\/td>\n<td>\n<ul>\n<li>Nausea<\/li>\n<li>Vomiting<\/li>\n<li>Emotional swings<\/li>\n<li>Anger or sadness<\/li>\n<li>Partial loss of understanding<\/li>\n<li>Impaired sensations<\/li>\n<li>Decreased libido<\/li>\n<li>Possibility of stupor<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul>\n<li>Severe motor impairment<\/li>\n<li>Loss of consciousness<\/li>\n<li>Memory blackout<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\">[latex]0.300\u20130.399[\/latex]<\/td>\n<td>\n<ul>\n<li>Stupor<\/li>\n<li>Central nervous system depression<\/li>\n<li>Loss of understanding<\/li>\n<li>Lapses in and out of consciousness<\/li>\n<li>Low possibility of death<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul>\n<li>Bladder function<\/li>\n<li>Breathing<\/li>\n<li>Dysequilibrium<\/li>\n<li>Heart rate<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\">[latex]0.400\u20130.500[\/latex]<\/td>\n<td>\n<ul>\n<li>Severe central nervous system depression<\/li>\n<li>Coma<\/li>\n<li>Possibility of death<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul>\n<li>Breathing<\/li>\n<li>Heart rate<\/li>\n<li>Positional Alcohol Nystagmus<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\">[latex]>0.50[\/latex]<\/td>\n<td>\n<ul>\n<li>High risk of poisoning<\/li>\n<li>High possibility of death<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul>\n<li>Life<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Joan likes to party and believes she is &#8220;just fine&#8221; when it comes to driving. At a\u00a0party, though, she downs\u00a0three standard drinks, one after the other, and then decides to leave. If Joan weighs [latex]135[\/latex] pounds, where would she be\u00a0on the table of the progressive effects of alcohol after\u00a0[latex]1.5[\/latex] hours? Would she be within the legal limit to drive home after this amount of time? Given any amount that she drinks, can you figure out how long she must wait\u00a0before she can drive safely and legally?<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1711\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>College Algebra: Inequalities. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Triangle Inequality. <strong>Authored by<\/strong>: By Brews ohare (Own work) . <strong>Provided by<\/strong>: Wikimedia Commons. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/creativecommons.org\/licenses\/by-sa\/3.0\">http:\/\/creativecommons.org\/licenses\/by-sa\/3.0<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"College Algebra: Inequalities\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Triangle Inequality\",\"author\":\"By Brews ohare (Own work) \",\"organization\":\"Wikimedia Commons\",\"url\":\"http:\/\/creativecommons.org\/licenses\/by-sa\/3.0\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"42239658-3246-4823-95cc-f9dc3ace8413","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1711","chapter","type-chapter","status-publish","hentry"],"part":1709,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/1711","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":22,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/1711\/revisions"}],"predecessor-version":[{"id":4899,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/1711\/revisions\/4899"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/parts\/1709"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/1711\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/media?parent=1711"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1711"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/contributor?post=1711"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/license?post=1711"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}