Section 3 – 6 Compound Inequalities

Objectives:To solve and graph inequalities

containing the word andTo solve and graph inequalities

containing the word or

Section 3 – 6

Compound Inequalities

Consists of two distinct inequalities joined by

the word and or the word or

Compound Inequality:

AND vs OR

Compound Inequalities Involving the word AND:

What compound inequality represents the phrase? Graph the solutions.a) 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.

Problem # 1 Writing a Compound Inequality

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

Write a compound inequality that represents the phrase. Graph the solutions.

1. All real numbers that are greater than or equal to -4 and less than 6

2. All real numbers that are less than or equal to 2.5 or greater than 6

Problem # 1 Got it?

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 Solving a Compound Inequality

Involving And

What are the solutions of -2 < x + 2 ≤ 5? Graph the solutions.

Problem # 2 Got it?

Solving AND compound inequalities simultaneously.

-2 < x + 2 ≤ 5

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 Writing & Solving a Compound

Inequality

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?

Problem # 3 Got it?

Textbook Page 204; #3, 9 –

16 All

Homework Assignment

Homework Answers

Compound Inequalities Involving the word 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 Solving a Compound Inequality

Involving OR

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

Problem # 4 Got it?

Used to describe an interval on the number

line, using three special symbols: Parenthesis: Brackets: Infinity:

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 Using Interval Notation

b) What are the solutions of 9 + 5n ≤ 5n – 1?

Problem # 5 Inequalities With Special

Solutions

1. What is the graph of (-2, 7]? How do you write (-

2, 7] as an inequality?

2. What is the graph of y > 7? How do you write y > 7 in interval notation?

Problem # 5 Got it?

3 – 6 Worksheet; Evens

Homework Assignment