SECTION 1-6 : ABSOLUTE VALUE EQUATIONS & INEQUALITIES ALGEBRA II HONORS/GIFTED - SECTION 1-6 (Absolute Value Equations and Inequalities) ALGEBRA II HONORS/GIFTED @ SECTION 1-6 : ABSOLUTE VALUE EQUATIONS & INEQUALITIES

1)a) If , then x = ? What is the definition of absolute value? x = 7 or x = -7 Distance from zero. b) If , then x = ? x = 23 or x = -23 Whatever comes out of the absolute value symbol can be positive or negative. c) If , then …… x < 9 and x > -9 d) If , then ….. x > 42 or x < -42

x = 2, -2 x = 3, -1 x = 4, 0 Solve and graph on a number line. 2) -2 2 -2 2 x = 2, -2 3) -1 3 x = 3, -1 4) 0 4 x = 4, 0 Quick, what’s the answer? 5) 1 5

6) -3 1 What’s the answer? 7) x = -3, 12 (number line too)

8) Awesome hint : anytime the variable appears on both sides, you may get extraneous solutions. CHECK YOUR ANSWERS!!!!! 5 only. -1 is extraneous The proverbial 5 second problem. Ready…… 9) No solutions. Absolute value can never equal a negative number! What happens if the right side equals zero?

Solve and graph each absolute value inequality over the Real numbers. 10) There are always TWO set-ups. 3x – 5 < 13 3x – 5 > -13 +5 +5 +5 +5 3x > -8 3x < 18 3 3 3 3 x < 6 Test each region to know where to shade. 6

11) Ok, let’s do an 8 second problem. 12) 15) 13) Now, for the 5 second problem. 14) 16)

17) A food manufacturer specifies that every family-size box of cereal should have a net weight of 25 ounces, with a tolerance of 1.2 ounces. Write and solve an absolute value inequality that describes the acceptable net weights for the cereal in a family-size box. Let w = weight of the cereal. Always start Then what? You want the weight to be exactly 25 ounces. However, the actual weight can be within 1.2 ounces either way of 25 ounces, So…. 23.8 < w < 26.2

18) You have found that your new winter coat is comfortable to wear when the outdoor temperature is between 10 degrees F and 42 degrees F inclusive. Write an absolute value inequality for this temperature range, where t represents the temperature in degrees Fahrenheit. IDEAS??? Since we have a range of numbers, find the middle number, 26. So, we have We want the range of temperatures to be within certain numbers. What inequality symbol do we use? < inclusive Less than or equals to what? What is the distance from 26 to 42 (or 10)? That’s it! So…

Need Help : http://www.youtube.com/watch?v=iI_2Piwn_og ALGEBRA II HONORS/GIFTED - SECTION 1-6 (Absolute Value Equations and Inequalities) Need Help : http://www.youtube.com/watch?v=iI_2Piwn_og http://www.youtube.com/watch?v=rC4bRSQetvQ http://www.youtube.com/results?search_query=absolute+value+inequalities&oq=absolute+value&gs_l=youtube.1.2.0l10.38547.43741.0.45397.14.9.0.5.5.0.109.818.6j3.9.0...0.0...1ac.1.11.youtube.UCCAoJ79G4k