Presentation on theme: "Compound Inequalities"— Presentation transcript:
1 Compound Inequalities What you’ll learnTo solve and graph inequalities containing the wordand. To solve inequalities containing the word orVocabularyCompound inequality: A compound inequalities consists of two distinct inequalities joined by the word and or the word or.Interval notation: includes the useof the three special symbols.
2 Writing a compound inequality Example 1:What compound inequality representsthe phrase? Graph the solutions.All real numbers that are greater than -2 andless than 6n›-2 and n‹6-2‹n and n‹6-2‹n‹6B. All real numbers that are less than 0 or greaterthan or equal to 5t‹0 or t≥5
3 Your turnWhat compound inequality represents the phrase? Graph the solutions.All real numbers that are greater than or equalto -4 and less than 6n≥-4 and n<6-4≤n<6B. All real numbers that are less than or equal toor greater than 6=2.5n≤2.5 or n>6
4 Solving a compound inequality involving and orNote: a solution of a compound inequality involvingand is any number that makes both inequalities true.You can solve this inequality both ways.
5 Solving a compound inequality involving or Note: A solution of a compound inequality involving oris an number that makes either inequality true.You must solve them separately.
6 Your turnWhat are the solutions of? Graph the inequalitiesA. -5 < 3y-4 < 14Answers:B.-2y+7 < 1 or 4y+3 ≤ -5Answers: y>3 or y≤2
7 the compound inequality Writing and Solving a Compound InequalityTo earn a B in your algebra course, you must achievean unrounded test average between 84 and 86,inclusive. You scored 86,85, and 80 on the first threetest of the grading period. What possible scores canyou earn on the fourth and final test a B in the courseNeedPossible scores youcan earnon the last test toget a B in the coursePlanWrite an expressionfor you test average.Then write and solvethe compound inequalityKnowTest average mustbe between 84 and 86,inclusive.The first 3 test scoresYour score on the fourth test must be between85 and 93, inclusive
8 Your turnTo win the recycling contest, you must collect between 83 and 87 pop tabs each week, inclusive. Suppose you collected 82, 86,and 84 pop tabs during the first three weeks of the competition. What are the possible numbers of pop tabs you can collect during the fourth and final week in order to win the recycling contest?Answer: between 80 and 96 pop tabs inclusive
9 Using Interval Notation 1.What is the graph [-4,6)? How do you write [-4,6)as an inequality?The parenthesis indicates that 6 is not included. So use an open circle at 6.The bracket indicatesthat -4 is included.So use a closedcircle at -4.-4 ≤ x < 62.What is the graph of x ≤ -1 or x>2? How do youwrite x≤-1 or x>2 in interval notation.The interval or