Solve the inequalities using Addition and Subtraction Section 6.1 Clickers #40 Education is a progressive discovery of our own ignorance. Will Durant.

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Presentation transcript:

Solve the inequalities using Addition and Subtraction Section 6.1 Clickers #40 Education is a progressive discovery of our own ignorance. Will Durant

The Concept At this point in our look at Algebra, we have dealt with solving first-order equations and linear systems At this point in our look at Algebra, we have dealt with solving first-order equations and linear systems We have discussed the concept of an inequality, but not dealt with them exclusively We have discussed the concept of an inequality, but not dealt with them exclusively Today we begin our look at inequalities and how to solve them Today we begin our look at inequalities and how to solve them

Definitions Inequality Inequality A mathematical sentence formed by placing one of the inequality symbols between two expressions A mathematical sentence formed by placing one of the inequality symbols between two expressions We can always see an inequality through it’s graph on a number line We can always see an inequality through it’s graph on a number line For example For example x<4 x<4 04

Definitions 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 How would we solve this? How would we solve this? Would we do this any differently? Would we do this any differently?

Addition & Subtraction Property Addition Property Adding the same number to each side of an equation produces an equivalent equation If x-a=b, then x-a+a=b+a, or x=b+a Subtraction Property Subtracting the same number to each side of an equation produces an equivalent equation If x+a=b, then x+a-a=b-a, or x=b-a Addition Property Adding the same number to each side of an equation produces an equivalent equation If x-a<b, then x-a+a<b+a, or x<b+a Subtraction Property Subtracting the same number to each side of an equation produces an equivalent equation If x+a<b, then x+a-a<b-a, or x<b-a Remember Chapter 3

Examples 18 24

Examples 17 88

Examples

Examples 22 20

Practical Example Answer: $88 or more You are shopping for bicycles. The type you want costs at least $185. You have saved $97. Find the possible amounts of money you need to save to buy the bicycle you want

Most Important Points What’s the most important thing that we can learn from today? We solve inequalities that involve addition and subtraction the same way that we handle equalities Graphing inequalities is easy!

Homework , 22-25, 31-36, even

Bellwork Is -9 a solution of a+7=-2? Is -9 a solution of a+7=-2? Solve the equation h+12=-8 Solve the equation h+12=-8 Write an inequality that describes the number of CDs you can buy for $12 each if you have no more than $60 to spend. Can you buy 6 CDs? Write an inequality that describes the number of CDs you can buy for $12 each if you have no more than $60 to spend. Can you buy 6 CDs?