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# PRECALC ALG & TRIG MAC 1147

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This 10 page Class Notes was uploaded by Marquise Graham on Saturday September 19, 2015. The Class Notes belongs to MAC 1147 at University of Florida taught by Hung Ngoc Nguyen in Fall. Since its upload, it has received 28 views. For similar materials see /class/207047/mac-1147-university-of-florida in Calculus and Pre Calculus at University of Florida.

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Date Created: 09/19/15

Lecture 6 Part I Section A6 Linear Inequalities An inequality is a statement that two quantities are not equal To solve an inequality is to nd all values of 1 that makes that the inequality true Unlike equations most inequality usually have an in nite number of solutions To present the solution we use interval notation Properties of Inequalities Let a b C and d be real numbers 1 Transitive Property If a lt b and b lt C then 2 Addition of Inequalities lfaltbandcltdthen 3 Addition Subtraction of a Constant If a lt b then 4 Multiplication Division by a Constant Forcgt 01fa lt b then Forclt 01fa lt b then NOTE To multiply or divide both sides of an inequality by a negative number reverse the inequality Solve the inequalities 1 3xlt9x4 2 1 2 1lt 2 5J 5 1 3 3 1lt 2 cg3 Inequalities Involving Absolute Value Recall is the distance from 1 to 0 on the number line Solve 1 lxllt1 2 lxlgt1 To Solve an Absolute Value Inequality If a is a nonnegative real number and 1 is an algebraic expression then M lt a if and only if M gt a if and only if Solve the inequalities 1 ix 5 lt 2 ie Find all numbers Within 2 units of 5 2 2 3 DIR is 4 3 x2 lt 10 4 2x1 2 5 Applications of Inequalities Find the domain of 1 in the expression v5 2 g In a math class there are 3 exams and a nal which counts twice as much as one exam If Sam scored 65 70 70 on the exams What is the lowest grade he needs on the nal to get a grade C in the course an average of 70 1 Suppose that a company can sell a new product for 19 If the cost to make the product is 8 per unit plus a xed cost of 88 how many items must the company sell in order to make a pro t 2 If one week the daily pro t from the sale of the items ranged from 44 to 110 over what range did daily sales yary that week Optional Material Reciprocal Properties for Inequalities 1 lfa gt 0 then a 1 lfa lt 0 then a lf0ltaltbthen 1 81 ltO ex ove23 4 2 ex SolveO lt lt 1 3 Lecture 6 Part II Section A7 Common Algebraic Errors Errors Involving Parentheses 1a I b7 a x b 2 ab27 a2b2 3 a b 7 ab lex 2Mxm2 Errors Involving Fractions a a a 1 b 1 b 96 2 1 ba l 1 1 1 3 abab 1 1 4n m 3 5 13x y 1 x2 6 2 y Errors Involving Exponents 1 x23 y 515 2 x2 x3 y x6 3 2x3 7 203 1 2 3 1 True or False xy Errors Involving Radicals 1 7 5 2 xx2a27 aa 3 Ja7 J a Errors Involving Dividing Out abx a 1 7amp1bx aax 2 ax 2 g Ememlkmx43i xy

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