Section 3 – 6 Compound Inequalities

Section 3 – 6 Compound Inequalities Objectives: To solve and graph inequalities containing the word and To solve and graph inequalities containing the word or

Compound Inequality: • Consists of two distinct inequalities joined by the word and or the word or

AND vs OR

Compound Inequalities Involving the word AND:

Problem # 1 Writing a Compound Inequality What compound inequality represents the phrase? Graph the solutions. • All real numbers that are greater than -2 and less than 6

Problem # 1 Writing a Compound Inequality What compound inequality represents the phrase? Graph the solutions. b) All real numbers that are less than 0 or greater than or equal to 5

Problem # 1 Writing a Compound Inequality What compound inequality represents the phrase? Graph the solutions. c) All real numbers that are greater than 1 and less than 5 d) All real numbers that are less than or equal to 10 or greater than 15

Problem # 1 Got it? Write a compound inequality that represents the phrase. Graph the solutions. • All real numbers that are greater than or equal to -4 and less than 6 • All real numbers that are less than or equal to 2.5 or greater than 6

Problem # 2 Solving a Compound Inequality Involving And a) What are the solutions of - 3 ≤ m – 4 < -1? Graph the solutions.

Problem # 2 Solving a Compound Inequality Involving And b) What are the solutions of - 2 < 3y – 4 < 14? Graph the solutions.

Problem # 2 Got it? What are the solutions of -2 < x + 2 ≤ 5? Graph the solutions.

Solving AND compound inequalities simultaneously. -2 < x + 2 ≤ 5

Problem # 3 Writing & Solving a Compound Inequality a) To earn a B in your algebra course, you must achieve an unrounded test average between 84 and 86, inclusive. You scored 86, 85, and 80 on the first three tests of the marking period. What possible scores can you earn on the fourth and final test to earn a B for the marking period?

Problem # 3 Writing & Solving a Compound Inequality b) To 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?

Problem # 3 Got it? To earn an A in your algebra course, you must achieve an unrounded test average between 94 and 96, inclusive. You scored 95, 90, and 99 on the first three tests of the marking period. What possible scores can you earn on the fourth and final test to earn an A for the marking period?

Homework Assignment • Textbook Page 204; #3, 9 – 16 All

Homework Answers

Compound Inequalities Involving the word OR:

Problem # 4 Solving a Compound Inequality Involving OR a)What are the solutions of 3t + 2 < -7 or -4t + 5 < 1? Graph the solutions.

Problem # 4 Solving a Compound Inequality Involving OR b)What are the solutions of -2y + 7 < 1 or 4y + 3 ≤ -5? Graph the solutions.

Problem # 4 Got it? What are the solutions of 2n – 1 < -3 or - 3n + 2 < - 4? Graph the solutions.

Interval Notation: • Used to describe an interval on the number line, using three special symbols: • Parenthesis: • Brackets: • Infinity:

Problem # 5 Using Interval Notation a)What is the graph of [-4, 6)? How do you write [-4, 6) as an inequality?

Problem # 5 Using Interval Notation b)What is the graph of x ≤ -1 or x > 2? How do you write x ≤ -1 or x > 2 in interval notation?

Problem # 5 Inequalities With Special Solutions b)What are the solutions of 9 + 5n ≤ 5n – 1?

Problem # 5 Got it? • What is the graph of (-2, 7]? How do you write (-2, 7] as an inequality? • What is the graph of y > 7? How do you write y > 7 in interval notation?

Homework Assignment • 3 – 6 Worksheet; Evens

Section 3 – 6 Compound Inequalities