Chapter 2: Equations and Inequalities Section 2.3/2.4: Conjunctions and Disjunctions and Solving Compound Sentences with Inequalities.

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Presentation transcript:

Chapter 2: Equations and Inequalities Section 2.3/2.4: Conjunctions and Disjunctions and Solving Compound Sentences with Inequalities

Section 2.3/2.4: Conjunctions/Disjunctions and Solving Compound Inequalities Goal: Students will be able to solve compound inequalities and graph the solution sets

Section 2.3/2.4: Conjunctions/Disjunctions and Solving Compound Inequalities Compound inequality – consists of two inequalities joined by the word and or the word or. ◦ To solve a compound inequality, you must solve each part of the inequality The graph of a compound inequality containing and is the intersection of the solution sets of the two inequalities ◦ Compound inequalities with and are called conjunctions ◦ Compound inequalities with or are called disjunctions

Section 2.3/2.4: Conjunctions/Disjunctions and Solving Compound Inequalities A compound inequality containing the word and is true if and only if both inequalities are true ◦ Example  x ≥ -1 and x < 2

Section 2.3/2.4: Conjunctions/Disjunctions and Solving Compound Inequalities Example 1 ◦ Solve 10 ≤ 3y – 2 < 19. Graph the solution set on a number line

Section 2.3/2.4: Conjunctions/Disjunctions and Solving Compound Inequalities The graph of a compound inequality containing or is the union of the solution sets of the two inequalities A compound inequality containing the word or is true if one or more of the inequalities is true ◦ Example  x ≤ 1 or x > 4

Section 2.3/2.4: Conjunctions/Disjunctions and Solving Compound Inequalities Example 2 ◦ Solve x + 3 < 2 or –x ≤ -4. Graph the solution set on a number line.

Section 2.3/2.4: Conjunctions/Disjunctions and Solving Compound Inequalities Example 3 ◦ Solve and graph the solution set for  2 (1 – 4x) > -3x – 13 and 3 (2x + 4) ≤ 24

Section 2.3/2.4: Conjunctions/Disjunctions and Solving Compound Inequalities Example 4 ◦ Solve and graph the solution set for  -2x ≥ -16 or 7x > 56

Section 2.3/2.4: Conjunctions/Disjunctions and Solving Compound Inequalities Example 5 ◦ Solve and graph the solution set for  5x > 25 and -2x ≥ 24

Section 2.3/2.4: Conjunctions/Disjunctions and Solving Compound Inequalities Homework: ◦ Practice Exercises: Pg. 65 #2-40 (even)