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Understanding Solutions of Equalities and Inequalities in Algebra

This lesson covers how to represent the solutions of equalities and inequalities using set notation and interval notation. Key examples demonstrate solving equations like 3x + 1 = 10 and 2x + 1 = 2x + 1, along with inequalities such as -2x + 4 > 8. Students will learn about unions and intersections of sets, along with how to graph them on number lines, and the significance of null sets. The session concludes with a focus on absolute value inequalities and preparing for upcoming assessments.

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Understanding Solutions of Equalities and Inequalities in Algebra

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  1. Algebra 2 Traditional 9-14-2012

  2. 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

  3. 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 { } ( )

  4. 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)

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

  6. 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

  7. 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”

  8. Pictorial Representations

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

  10. Union and Intersection on the number line • Union • x<4 OR x>0 • Intersection • x<4 AND x>0

  11. Absolute Value Inequalities • Everything you EVER wanted to know about |2x-3|=, <, or > 9!

  12. 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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