1.7a - Absolute Value Inequalities PAGE 45 3) 5) 7) 9) 11) –3 < x < 1; x > –3 AND x < 1 13) x < –2 OR x > 4 15) C 23) x < –2; {x|x < –2} (-∞, -2] 25) x < 4; {x|x < 4} (-∞, 4) 27) x < 6; {x|x < 6} (-∞, 6] 29) x < –8; {x|x < 4} 31) x < 1/2; {x|x < 1/2} (-∞, ½) 4 4 33) x < –7; {x|x < –7} (-∞, –7) 35) The inequality should not be reversed when subtracting 37) –6 < x < 3; {x|–6 < x < 3}; (-6, 3) 39) 1 < x < 7; {x|1 < x < 7} [1, 7) –7 –5 6 6 –3.5 –6 –8 3 1 7 –2 1/2 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities PAGE 45 41) –3/2 < x < –1/2; {x|–3/2 < x < –1/2}; (-3/2, –1/2) 43) x < –4 OR x > 2; {x|x < –4 OR x > 2}; (-3/2, –1/2) 45) x < –1/2 OR x > 1; {x|x < –1/2 OR x > 1}; [-1/2, 1] 49) No Solution 50) All Real Numbers 51) 53) 45x + 35 < 250; x < 4 7/9 days 56) D –3/2 –1/2 –4 2 –1/2 1 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities ABS VALUE 23. Neither 25. Parallel 26. 27. 29. 31. 33. y = 21x – 40 35. y = 1/6x + 4/3 37. y = –3x – 8 38. Park Place 13. 15. m = 2/3 17. 19a. 20. 21. 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 Absolute Value Inequalities Section 1.7a 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 Steps Identify whether it is an AND/OR inequality Write both equations with one with the regular sign and other equation with the sign SWITCHED with OPPOSITE number Solve each inequality and write answer in inequality and/or interval notation Check each solution and make sure there aren’t any extraneous solutions Graph appropriately on number line 6 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

Solving Absolute Value Inequalities 12/27/2018 Solving Absolute Value Inequalities When Solving for Inequalities, remember: Less ThAND GreatOR Than Less Than, “AND” Greater Than, “OR” 7 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 Example 1 Solve |x + 3| < 5 and graph the solution on a number line. | 2 | –8 | 8 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 Example 2 Solve |4x + 5| > 13 and graph the solution on a number line. | 2 | –9/2 | 9 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 Example 3 Solve |1/7x + 2| – 5 < 3 and graph the solution on a number line. | 42 | –70 | 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 YOUR TURN Solve |2x – 5| > x + 1 and graph the solution on a number line. | 4/3 6 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 Example 4 Solve 3|12 – 4x|+ 4 < 28 and graph the solution on a number line. 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 Example 4 Solve 3|12 – 4x|+ 4 < 28 and graph the solution on a number line. | | 1 | 5 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 Example 5 Solve 8|x + 4|> 48 and graph the solution on a number line. | –10 | –2 | 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 Example 6 Solve and graph the solution on a number line. | –8 | | 4 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 YOUR TURN Solve and graph the solution on a number line. | –8 | | 1 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 Example 7 Solve |2x – 1| < –25 and graph the solution on a number line. | No Solution 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 Example 8 Solve |x + 1| > –16 and graph the solution on a number line. | All Real Numbers 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 Your Turn Solve –2|x + 4| < 22 and graph the solution on a number line. | No Solution 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

Absolute Value Applications 12/27/2018 Absolute Value Applications To write the equation: |actual amount – ideal amount| < tolerance Tolerance is the max accepted deviation of an item from some ideal or mean Tolerance = (High End) – (Avg of Low and High Ends) If the problem is “within range,” apply < (AND), “acceptable” If the problem is “out of range,” apply > (OR), “unacceptable” 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 Example 9 A manufacturer has a 0.6oz tolerance for a bottle of salad dressing advertised as 16oz. Write and solve an absolute value inequality that describes the acceptable volumes for “16oz” bottles. 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 Example 10 A manufacturer has a tolerance of 0.36 lb for a bag of potting soil advertised as 9.6 lb. Write and solve an absolute value inequality that describes unacceptable weights for “9.6 lb” bags. 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 YOUR TURN A food manufacture 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. 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities

1.7a - Absolute Value Inequalities 12/27/2018 Assignment Worksheet 12/27/2018 5:10 AM 1.7a - Absolute Value Inequalities