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Published byErick Carpenter Modified over 9 years ago

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Algebra 2 Traditional 9-14-2012

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RFA 9-14 1) Solve the following absolute value equality: 2+|x-8| = 3x-6 2) Solve the following inequalities and graph the solution sets ◦ 9(2x+3)>10 ◦ 7-2m ≥ 0

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Representing the solutions of equalities You can think of the solution(s) to a given equation as solution sets. Equation Set notation Interval notation 3x+1 = 10 2x + 1 = 2x + 1 3x+4 = 3x – 7

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Representing the solutions of equalities You can think of the solution(s) to a given equation as solution sets. Equation Set notation Interval notation 3x+1 = 10 {3} [3] 2x + 1 = 2x + 1 {x| x is a real number} 3x+4 = 3x – 7 { } ( )

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Representing the solutions of in-equalities -2x + 4 > 8 -2x > 4 X < -2 {x| x<-2} (set builder notation) (-∞, -2) (interval notation) Number line (Draw below)

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Quick final note… If an inequality includes an “or equal to” part, that part remains even if you need to flip the inequality.

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Before the next section: Operations with Sets Goals: ◦ Know what it means to find the “intersection” and “union” between multiple sets. ◦ Be able to graph unions and intersections on number lines ◦ Define what an empty set, or “null” set is

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Union & Intersections Union: the set of elements in one set, another, or both means the union of sets “A” and “B” Intersection: The set of elements that are in two sets at the same time means the intersection of sets “F” and “G”

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Pictorial Representations

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Null or Empty Sets Sets with no elements in them are called null or empty sets. { } OR

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Union and Intersection on the number line Union x 0 Intersection x 0

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Absolute Value Inequalities Everything you EVER wanted to know about |2x-3|=, 9!

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Type of Absolute Value Problem |ax+b| What it means in terms of distance What kind of solution you are going to get |ax+b|=k A specific distance “k” (to the left or right) away from zero on number line |ax+b|>k Two inequalities that won’t overlap (so link them with a “U”) |ax+b|<k ax+b is BETWEEN “k” distance from zero to the left and “k” distance to the right

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Type of Absolute Value Problem |ax+b| What it means in terms of distance What kind of solution you are going to get |ax+b|=k A specific distance “k” (to the left or right) away from zero on number line Two specific solutions (assuming k>0) |ax+b|>k ax+b must be AT LEAST “k” distance away from zero on number line Two inequalities that won’t overlap (so link them with a “U”) |ax+b|<k ax+b is BETWEEN “k” distance from zero to the left and “k” distance to the right Two inequalities that intersect, so find the intersection interval

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Group Work/HW Group Work: 1.7 1-14 Homework 1.7 15-43 odd Test early next week on chapter 1!

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