Solve the inequalities using Solve the inequalities using Addition and SubtractionAddition and Subtraction

Section 6.1Section 6.1

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#40 Education is a progressive discovery of our own ignorance.

Will Durant

The ConceptThe Concept

At this point in our look at Algebra, we have dealt with At this point in our look at Algebra, we have dealt with solving first-order equations and linear systemssolving first-order equations and linear systems

We have discussed the concept of an inequality, but We have discussed the concept of an inequality, but not dealt with them exclusivelynot dealt with them exclusively

Today we begin our look at inequalities and how to Today we begin our look at inequalities and how to solve themsolve them

DefinitionsDefinitions

InequalityInequality A mathematical sentence formed by placing one of the A mathematical sentence formed by placing one of the

inequality symbols between two expressionsinequality symbols between two expressions

We can always see an inequality through it’s graph on We can always see an inequality through it’s graph on a number linea number line

For exampleFor example x<4x<4

0 4

DefinitionsDefinitions

SymbolsSymbols Greater thanGreater than Less thanLess than Greater than or equal toGreater than or equal to Less than or equal toLess than or equal to

Does not include the number

Include the number

Open Circle

Closed Circle

Solving InequalitiesSolving Inequalities How would we solve this?How would we solve this?

Would we do this any differently?Would we do this any differently?

2

53

x

x

2

53

x

x

Addition & Subtraction PropertyAddition & 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

ExamplesExamples

3 21x

211x

5033x

1910 x

. 18

. 18

. 24

A x

B x

C x

18

18

24

ExamplesExamples

211x

33 50x

1910 x

. 17

. 17

. 88

A x

B x

C x

17

17

88

ExamplesExamples

19 10x . 9

. 9

. 29

A x

B x

C x

-9

-9

-29

ExamplesExamples

21 1x .22

.22

.20

A x

B x

C x

22

22

20

Practical ExamplePractical Example

97 185a

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

88a

Most Important PointsMost Important Points What’s the most important thing that we can learn What’s the most important thing that we can learn

from today?from today? We solve inequalities that involve addition and subtraction the We solve inequalities that involve addition and subtraction the

same way that we handle equalitiessame way that we handle equalities Graphing inequalities is easy!Graphing inequalities is easy!

HomeworkHomework

6.16.1

1-17, 22-25, 31-36, 40-50 even 1-17, 22-25, 31-36, 40-50 even

BellworkBellwork

Is -9 a solution of a+7=-2?Is -9 a solution of a+7=-2? Solve the equation h+12=-8Solve the equation h+12=-8 Write an inequality that describes the number Write an inequality that describes the number

of CDs you can buy for $12 each if you have no of CDs you can buy for $12 each if you have no more than $60 to spend. Can you buy 6 CDs?more than $60 to spend. Can you buy 6 CDs?