Why It Matters: Linear Inequalities
Why learn to solve linear equations and inequalities?
You might be surprised to learn that applications of linear equations turn up in many places besides math classrooms. Knowing how to solve them is a basic math 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 addition and subtraction. To see a linear equation in action, let's consider one that's used by forensic scientists to calculate blood alcohol content. Not surprisingly, blood alcohol content (BAC) is a measurement of how much alcohol is in someone’s blood. It's usually measured in grams, as a percentage. For example, a BAC of [latex]0.30\%[/latex] is threetenths of [latex]1\%[/latex], and it indicates that there are [latex]3[/latex] grams of alcohol for every [latex]1,000[/latex] grams of blood—which is actually a lot. A BAC of [latex]0.05\%[/latex] impairs reasoning and the ability to concentrate. A BAC of [latex]0.30\%[/latex] 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 [latex]0.08\%[/latex]. BAC is usually determined by the results of a breathalyzer, urinalysis, or blood test. Swedish physician E. M. P. Widmark developed an equation that works well for estimating BAC without using one of those tests. Widmark's formula is widely used by forensic scientists:[latex]B[/latex] = [latex]0.015t +\left(\frac{2.84N}{Wg}\right)[/latex]
where
 [latex]B[/latex] = percentage of BAC
 [latex]t[/latex] = number of hours since the first drink
 [latex]N[/latex] = number of “standard drinks” (a standard drink is one [latex]12[/latex]ounce beer, one [latex]5[/latex]ounce glass of wine, or one [latex]1.5[/latex]ounce shot of liquor). [latex]N[/latex] should be at least [latex]1[/latex].
 [latex]W[/latex] = weight in pounds
 [latex]g[/latex] = gender constant: [latex]0.68[/latex] for men and [latex]0.55[/latex] for women
Progressive effects of alcohol  

BAC (% by vol.)  Behavior  Impairment 
[latex]0.001[/latex]–[latex]0.029[/latex] 


[latex]0.030[/latex]–[latex]0.059[/latex] 


[latex]0.060[/latex]–[latex]0.099[/latex] 


[latex]0.100[/latex]–[latex]0.199[/latex] 


[latex]0.200[/latex]–[latex]0.299[/latex] 


[latex]0.300[/latex]–[latex]0.399[/latex] 


[latex]0.400[/latex]–[latex]0.500[/latex] 


>[latex]0.50[/latex] 


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 Balancing Blood Alcohol. Authored by: Carnegie Foundation, Pierce College. Located at: https://s3.amazonaws.com/wamapdata/cfiles/10722/M96F16stu.pdf. License: CC BYNCSA: AttributionNonCommercialShareAlike. License terms: Revisions by Pierce College.
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