solve the inequalities using addition and subtraction section 6.1 clickers #40 education is a...
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Solve the inequalities using Solve the inequalities using Addition and SubtractionAddition and Subtraction
Section 6.1Section 6.1
Clickers
#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
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!
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?