AT100 - Introductory Algebra. Section 2.7: Inequalities. x a. x a. x < a

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1 Section 2.7: Inequlities In this section, we will Determine if given vlue is solution to n inequlity Solve given inequlity or compound inequlity; give the solution in intervl nottion nd the solution 2.7 Inequlities Exmple: Tell whether ech numer is solution of 3x+ 7< 4x 2 x = 12 x = -6 x = 0 x = Determine if Given Vlue is Solution to n Inequlity An unounded intervl is n intervl tht extends forever in one direction. inequlity nottion of solution set intervl nottion x > x x < x ll rel numers x A liner inequlity in one vrile (sy, x) is ny inequlity tht cn e expressed in one of the following forms, where,, c re rel numers 0 x + < c x + c x + > c x + c AT100 - Introductory Alger

2 AT100 - Introductory Alger Property 1 of Inequlities: Any rel numer cn e dded (or sutrcted) from oth sides of n inequlity. This produces n equivlent inequlity. exmple: - 4 < 6 Property 2 of Inequlities: Both sides of n inequlity cn e multiplied (or divided) y positive numer. This produces n equivlent inequlity. exmple: - 4 < 6 Property 3 of Inequlities: If oth sides of n inequlity re multiplied (or divided) y negtive numer, nother inequlity results (opposite direction). exmple: - 4 < 6 Exmple: Solve the inequlity. Grph the solution set nd express your x 9> 3 intervl nottion Exmple: Solve the inequlity. Grph the solution set nd express your r intervl nottion

3 AT100 - Introductory Alger Exmple: Solve the inequlity. Grph the solution set nd express your 3x+ 7 4x 2 intervl nottion Exmple: Solve the inequlity. Grph the solution set nd express your 17(3 x) 3 13x intervl nottion Exmple: Solve the inequlity. Grph the solution set nd express your 1 c 3 + > intervl nottion

4 Exmple: Solve the inequlity. Grph the solution set nd express your -2/9 5x/6 1/3 intervl nottion A compound inequlity is connected pir of inequlities. Note tht doule inequlity is ssumed to e compound inequlity contining the word nd. i.e. c< x< d mens c< x nd x< d inequlity nottion of solution set intervl nottion open intervls: < x< hlf-open intervls: x< < x closed intervls: x Exmple: Solve the inequlity. Grph the solution set nd express your - 8 < x 8 < 8 intervl nottion AT100 - Introductory Alger

5 AT100 - Introductory Alger Exmple: Solve the inequlity. Grph the solution set nd express your 3< 3 2x < 9 intervl nottion Exmple: Solve the inequlity. Grph the solution set nd express your 1 7x intervl nottion Exmple: Before tking on client, n employment gency requires the pplicnt to verge t lest 70% on ttery of jo skill tests. If n pplicnt scored 70%, 74%, nd 84% on the first three exms, wht must he score on the fourth test to mintin 70% or etter verge?

6 Independent Prctice You lern mth y doing mth. The est wy to lern mth is to prctice, prctice, prctice. The ssigned homework exmples provide you with n opportunity to prctice. Be sure to complete every ssigned prolem (or more if you need dditionl prctice). Check your nswers to the odd-numered prolems in the ck of the text to see whether you hve correctly solved ech prolem; rework ll prolems tht re incorrect. Red pp Homework: pp #5, 13, odds, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 87, 91, Inequlities AT100 - Introductory Alger

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