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Chapter 5.5 Solving Open Sentences With Absolute Values Check 3102.3.14 Solve absolute value equations and inequalities (including compound inequalities) with one variable and graph their solutions on a number line. and 3102.3.18 Analyze the characteristics of graphs of basic linear relations and linear functions including constant function, direct variation, identity function, vertical lines, absolute value of linear functions. Use technology where appropriate. Review Franklin D. Roosevelt: It is common sense to take a method and try it. If it fails, admit it frankly and try another. But above all, try something. • Define Absolute Value • What is the absolute value of the following: |20| |-25| |x| |-a| 20 25 x a Absolute Value Inequalities |x| = 5 0 {x|-5<x<5} Solve Absolute Value Equation |a - 4|= 3 a - 4= 3 + 4= +4 a=7 Two Solutions to Absolute Value Equations 1. Value Inside Symbols is positive 2. Value inside symbols is negative a - 4= -3 + 4= +4 a=1 Solve Absolute Value Equation |t + 5|< 9 t + 5< 9 - 5 -5 t<4 Two Solutions to Absolute Value Equations 1. Value Inside Symbols is positive 2. Value inside symbols is negative with the opposite sign t + 5 > -9 - 5 -5 t > -14 Solve Absolute Value Equation |3y -3|> 9 3y -3> 9 +3 +3 Two Solutions to Absolute Value Equations 1. Value Inside Symbols is positive 2. Value inside symbols is negative 3y -3 < -9 +3 +3 3y > 12 3y < -6 y>4 y < -2 Word Problems - Inequalities • pH of a buffered eye solution must be within 0.002 of a pH of 7.3 7.298 ph 7.302 Word Problems - Inequalities • The average length of a human pregnancy is 280 days. However, a healthy, full-term pregnancy can be 14 days longer or shorter. Write an absolute value inequality for the length of a full-term pregnancy. 266 pregnancy 294 • Solve the inequality for the length of a full-term pregnancy. Graph your results. 266 294 Practice • Page 312, 8 – 40 even*