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4.6 Absolute Value Equations and Inequalities Solving Absolute Value Equations absolute value - Ex 1: Solve |a| – 3 = 5 Ex 2: Solve 3|x|= 15 Guided Practice Solve each equation. Check your solution. 1. |t| - 2 = -1 2. 4 = 3|w| - 2 3. Is there a solution of 2|n| = -15. Explain. Ex 3: Solve |3c - 6| = 9. Check your solution. Ex 4: Solve |4d + 8| = 36. Check your solution. Guided Practice Solve each equation. Check your solution. 1. |c - 2| = 6 2. |2d| + 3 = 21 3. |7x| = 14 Homework: Pages 237 - 238 # 1-17 odd, 18-20 Solving Absolute Value Inequalities Absolute value inequalities can be written as compound inequalities. |n – 2| < 5 |n – 2| > 5 Ex 3: Solve |y – 5| ≤ 2. Graph the solutions. Ex 4: Solve |2y – 3| > 7. Graph the solution. 3 Solving Absolute Value Inequalities Get the absolute value expression alone on one side of the inequality Use the Addition, Subtraction, Multiplication, and Division properties to get the absolute value expression alone on one side of the inequality. - 6|w - 3| + 6 < - 18 Solve each inequality. Graph the solution. 1. |2n + 3| ≤ 5 2. 5 > |v + 2| + 3 3. 3|2x| ≥ 12 1 Ex 4: The ideal diameter of a piston for one type of car is 88.000 mm. The actual diameter can vary from the dial by at most 0.007 mm. Find the range of acceptable diameters for the piston. Guided Practice 1. Solve and graph |w + 2| > 5 2. Solve and graph 3|x + 4| ≤ 15 3. The ideal weight of one type of model airplane engine is 33.86 ounces. The actual weight may vary from the ideal by at most 0.05 ounce. Find the range of acceptable weights for this engine. Homework: Pages 238 - 239 #25 - 35 odd, 37, 41 - 45, 53, 55, 56