Two-Variable Inequalities Essay

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Two-Variable Inequalities Tammy Davis MAT 222 William Blasczyk August 25, 2014 Two-Variable Inequalities A compound inequality in two variables consists of two simple inequalities joined with “and” or “or.” In real word applications, the x and y variables, usual represent amounts, or measurements of some type. Linear inequalities are used in a variety of applications across several industries. Examples include: budget planning for any business or household; an interior designer determining which pieces of furniture would fit into a room, determining shipping restrictions; or a doctor calculating someone's BMI as a measure of health. The important thing to note about real world applications is that their solution sets cannot equal a negative number. (Dugopolski, 2012) PART ONE Shipping restrictions. The accompanying graph shows all of the possibilities for the number of refrigerators and the number of TVs that will fit into an 18-wheeler. a.) Write an inequality to describe this region. To do this, first, we must find the slope for the given test points, (110,0) and (0, 330). The equation for slope is =y2-y1x2-x1 , or (m = rise/run), so … m = 330−(0)/0−(110) Multiply by -1 to get rid of parentheses m = −330/110 Cancel out the common factor of 110, and simplify m = -3 Next, find the equation of the line using y=mx+b y = (−3)⋅x+b Input the points of x and y (0) = (−3)⋅(110)+b Multiply 0 = b−330 Solve for b b = 330 So, the equation of the line is … y = −3x+330 Next, multiply by -1 to get the inequality 3x+y ≤ 330 Final answer The graph will have a solid line instead of a dashed line. b.) Will the truck hold 71 refrigerators and 118 TVs? First, we need to make x = 71 and y = 118; this is our test point – (71, 118) 3(71)+118 ≤ 330 Input the values, then simplify 331

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