Use interval notation to indicate the graphed numbers. Warm-Up Use interval notation to indicate the graphed numbers. (-2, 3] (-, 1]

2-8: Solving Absolute-Value Equations and Inequalities Warning: Take noTes On the sheet provided. Completely fill-in and Show To Ms. Lagroon at the End of the period for full class Work Credit 30%. 2-8: Solving Absolute-Value Equations and Inequalities Part 1: Solving Compound Inequalities - Disjunctions

Compound inequality – 2 or more inequalities Disjunction - compound inequality that uses the word or. Has 2 separate pieces.

Identifying Disjunctions *3 Categories* Category Description Inequalities The word “OR” is between 2 inequalities Number line graph Two separate graphs Set-builder Notation 2 inequalities are separated by the symbol U (union) x ≤ –3 OR x > 2 Set builder notation: {x|x ≤ –3 U x > 2}

*Determine whether the example is a disjunction or not a disjunction* Identifying Disjunctions *Determine whether the example is a disjunction or not a disjunction* 6y < –24 OR y +5 ≥ 3 Disjunction x ≥ –3 AND x < 2 Not a Disjunction x – 5 < –2 OR –2x ≤ –10

*Determine whether the example is a disjunction or not a disjunction* Identifying Disjunctions *Determine whether the example is a disjunction or not a disjunction* –3 –2 –1 0 1 2 3 4 5 6 Disjunction –6 –5 –4 –3 –2 –1 0 1 2 3 Not a Disjunction –6 –5 –4 –3 –2 –1 0 1 2 3

*Determine whether the example is a disjunction or not a disjunction* Identifying Disjunctions *Determine whether the example is a disjunction or not a disjunction*

Solving & Graphing Disjunctions Step 1 Solve each inequality for the variable. Step 2 Graph both solutions on the number line. Step 3 Write you answer in set-builder notation. Step 4 Write you answer in interval notation.

Solve the compound inequality. Then graph the solution set. Example 1 Solve the compound inequality. Then graph the solution set. 6y < –24 OR y +5 ≥ 3 Solve both inequalities for y. 6y < –24 y + 5 ≥3 or y < –4 y ≥ –2 The solution set is all points that satisfy {y|y < –4 U y ≥ –2}. –6 –5 –4 –3 –2 –1 0 1 2 3 (–∞, –4) U [–2, ∞)

Solve the compound inequality. Then graph the solution set. Example 2 Solve the compound inequality. Then graph the solution set. x – 5 < –2 OR –2x ≤ –10 Solve both inequalities for x. x – 5 < –2 or –2x ≤ –10 x < 3 x ≥ 5 The solution set is the set of all points that satisfy {x|x < 3 U x ≥ 5}. –3 –2 –1 0 1 2 3 4 5 6 (–∞, 3) U [5, ∞)

Solve the compound inequality. Then graph the solution set. Example 3 Solve the compound inequality. Then graph the solution set. x – 2 < 1 OR 5x ≥ 30 Solve both inequalities for x. x – 2 < 1 5x ≥ 30 or x ≥ 6 x < 3 The solution set is all points that satisfy {x|x < 3 U x ≥ 6}. –1 0 1 2 3 4 5 6 7 8 (–∞, 3) U [6, ∞)

Solve the compound inequality. Then graph the solution set. Example 4 Solve the compound inequality. Then graph the solution set. x –5 < 12 OR 6x ≤ 12 Solve both inequalities for x. x –5 < 12 or 6x ≤ 12 x < 17 x ≤ 2 Because every point that satisfies x < 2 also satisfies x < 2, the solution set is {x|x < 17}. 2 4 6 8 10 12 14 16 18 20 (-∞, 17)

In tribes complete the worksheet! For each question: Solve Graph Write in set-builder Write in interval Exit Slip: Define disjunction. Give me an example of a disjunction and an example of something that is not a disjunction.