{"id":4395,"date":"2016-10-03T20:51:20","date_gmt":"2016-10-03T20:51:20","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/?post_type=chapter&#038;p=4395"},"modified":"2018-05-16T23:02:24","modified_gmt":"2018-05-16T23:02:24","slug":"introduction-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/chapter\/introduction-2\/","title":{"raw":"Why solve linear equations and inequalities?","rendered":"Why solve linear equations and inequalities?"},"content":{"raw":"<img class=\"wp-image-1644 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/14224321\/6039407489_44a996a977_o-576x1024.jpg\" alt=\"Photo of a mai tai\" width=\"225\" height=\"400\" \/>\r\n\r\nYou might be surprised to learn\u00a0that applications of\u00a0linear equations turn up\u00a0in many places besides math classrooms. Knowing how to solve them is a\u00a0basic\u00a0math skill used in nearly every academic discipline and in many jobs. One of the fundamental principles of solving linear equations is that of reversing or undoing mathematical operations such as\u00a0addition and subtraction. To see a linear equation in action, let's consider\u00a0one\u00a0that's used by forensic scientists to calculate blood alcohol content.\r\n\r\nNot surprisingly, blood alcohol content (BAC) is a measurement of how much alcohol is in someone\u2019s blood. It's usually measured in grams and as a percentage. For example, a BAC of 0.30% is three-tenths of 1%, and it indicates\u00a0that there are 3 grams of alcohol for every 1,000 grams of blood\u2014which is actually a lot. A BAC of 0.05% impairs reasoning and the ability to concentrate. A BAC of 0.30% can lead to a blackout, shortness of breath, and loss of bladder control. In most states, the legal limit for driving is a BAC of 0.08%.\r\n\r\nBAC is usually determined by the results of a breathalyzer, urinalysis, or blood test. Swedish physician E. M. P. Widmark developed an\u00a0equation that works well for estimating BAC without using one of those tests. Widmark's formula is widely used by forensic scientists:\r\n\r\n[latex]\\text{B} = -0.015t +\\left(\\frac{2.84N}{Wg}\\right)[\/latex]\r\n\r\nwhere\r\n<ul>\r\n \t<li>B = percentage of BAC<\/li>\r\n \t<li>t = number of hours since the first drink<\/li>\r\n \t<li>N = number of \u201cstandard drinks\u201d (a standard drink is one 12-ounce beer, one 5-ounce glass of wine, or one 1.5-ounce shot of liquor). N should be at least 1.<\/li>\r\n \t<li>W = weight in pounds<\/li>\r\n \t<li>g = gender constant: 0.68 for men and 0.55 for women<\/li>\r\n<\/ul>\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 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\">0.001\u20130.029<\/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\">0.030\u20130.059<\/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\">0.060\u20130.099<\/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\">0.100\u20130.199<\/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\">0.200\u20130.299<\/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\">0.300\u20130.399<\/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\">0.400\u20130.500<\/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\">&gt;0.50<\/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 135 pounds, where would she be\u00a0on the table of the progressive effects of alcohol after 1.5 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? At the end of the module, we will return to Joan and see if we can use our knowledge of algebra to help her make a safe choice.\r\n\r\n&nbsp;","rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1644 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/14224321\/6039407489_44a996a977_o-576x1024.jpg\" alt=\"Photo of a mai tai\" width=\"225\" height=\"400\" \/><\/p>\n<p>You might be surprised to learn\u00a0that applications of\u00a0linear equations turn up\u00a0in many places besides math classrooms. Knowing how to solve them is a\u00a0basic\u00a0math skill used in nearly every academic discipline and in many jobs. One of the fundamental principles of solving linear equations is that of reversing or undoing mathematical operations such as\u00a0addition and subtraction. To see a linear equation in action, let&#8217;s consider\u00a0one\u00a0that&#8217;s used by forensic scientists to calculate blood alcohol content.<\/p>\n<p>Not surprisingly, blood alcohol content (BAC) is a measurement of how much alcohol is in someone\u2019s blood. It&#8217;s usually measured in grams and as a percentage. For example, a BAC of 0.30% is three-tenths of 1%, and it indicates\u00a0that there are 3 grams of alcohol for every 1,000 grams of blood\u2014which is actually a lot. A BAC of 0.05% impairs reasoning and the ability to concentrate. A BAC of 0.30% can lead to a blackout, shortness of breath, and loss of bladder control. In most states, the legal limit for driving is a BAC of 0.08%.<\/p>\n<p>BAC is usually determined by the results of a breathalyzer, urinalysis, or blood test. Swedish physician E. M. P. Widmark developed an\u00a0equation that works well for estimating BAC without using one of those tests. Widmark&#8217;s formula is widely used by forensic scientists:<\/p>\n<p>[latex]\\text{B} = -0.015t +\\left(\\frac{2.84N}{Wg}\\right)[\/latex]<\/p>\n<p>where<\/p>\n<ul>\n<li>B = percentage of BAC<\/li>\n<li>t = number of hours since the first drink<\/li>\n<li>N = number of \u201cstandard drinks\u201d (a standard drink is one 12-ounce beer, one 5-ounce glass of wine, or one 1.5-ounce shot of liquor). N should be at least 1.<\/li>\n<li>W = weight in pounds<\/li>\n<li>g = gender constant: 0.68 for men and 0.55 for women<\/li>\n<\/ul>\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 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\">0.001\u20130.029<\/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\">0.030\u20130.059<\/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\">0.060\u20130.099<\/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\">0.100\u20130.199<\/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\">0.200\u20130.299<\/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\">0.300\u20130.399<\/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\">0.400\u20130.500<\/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\">&gt;0.50<\/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 135 pounds, where would she be\u00a0on the table of the progressive effects of alcohol after 1.5 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? At the end of the module, we will return to Joan and see if we can use our knowledge of algebra to help her make a safe choice.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"author":21,"menu_order":1,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4395","chapter","type-chapter","status-publish","hentry"],"part":359,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4395","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4395\/revisions"}],"predecessor-version":[{"id":5258,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4395\/revisions\/5258"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/359"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4395\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/wp\/v2\/media?parent=4395"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=4395"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/wp\/v2\/contributor?post=4395"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/wp\/v2\/license?post=4395"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}