Solve compound inequalities Section 6.4 #43 The continuum is that which is divisible into indivisibles that are infinitely divisible. Physics. Aristotle

Concept The first three sections of this chapter dealt primarily with inequalities that are single sided The first three sections of this chapter dealt primarily with inequalities that are single sided Today we’re going to talk about compound, or double sided, inequalities Today we’re going to talk about compound, or double sided, inequalities

Definitions Don’t write this down…just review Symbols Symbols Greater than Greater than Less than Less than Greater than or equal to Greater than or equal to Less than or equal to Less than or equal to Does not include the number Include the number Open Circle Closed Circle

Solving Inequalities Sometimes we have to realize that our inequalities are bounded Sometimes we have to realize that our inequalities are bounded For instance, if we were writing an equation for today’s temperature, we’d say that it has to be between 40 degrees and 26 degrees For instance, if we were writing an equation for today’s temperature, we’d say that it has to be between 40 degrees and 26 degrees Or we could say that it is less than or equal to 40 and greater than or equal to 26 Or we could say that it is less than or equal to 40 and greater than or equal to 26 We would express this compound inequality this way We would express this compound inequality this way

Solving Inequalities As well, we can express an inequality that is bounded the other way. As well, we can express an inequality that is bounded the other way. For instance, if we were going to talk about the temperatures that we don’t want a substance to be under, we could say that it needs to be either below 2 degrees C or above 50 degrees C For instance, if we were going to talk about the temperatures that we don’t want a substance to be under, we could say that it needs to be either below 2 degrees C or above 50 degrees C We would express this compound inequality this way We would express this compound inequality this way

Solving Inequalities There for we can explain that AND statements can be expressed as either There for we can explain that AND statements can be expressed as either and OR statements can be expressed as and OR statements can be expressed as or

Solving Inequalities To solve these we simply solve them twice To solve these we simply solve them twice Because this is an AND statement we can either combine or leave separate

Solving Inequalities To solve these we simply solve them twice To solve these we simply solve them twice Because it’s an OR statement, we have to leave it an OR statement

Graphing We often talk about the concept that AND statements converge We often talk about the concept that AND statements converge Therefore OR statements diverge Therefore OR statements diverge

Example Solve for x Solve for x

Example

Examples

Examples

Examples

Last Example You estimate you can read at least 8 history text pages per day. What are the possible numbers of days it will take you to read at most 118 pages?

Most Important Points Difference between an and statement and an or statement Difference between an and statement and an or statement How to solve compound inequalities How to solve compound inequalities How to graph compound inequalities How to graph compound inequalities

Homework , 23-27, 47-50, 55