general math unit 5...
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General MathUnit 5 – InequalitiesStandards Addressed:
Solve equations and inequalities arising from a context.
Solve equations and inequalities using algebraic manipulation.
A little Review
• Solve each equation. Show your steps and check your answer.
1.
2.
3.
213 x
3684 x
5)3(229 x
U5D1
Inequalities!
•Vocab: An Inequality is a comparison of two values that may or may not be equal.
U5D1
Inequalities!
•Example
Place these values on a number line and compare their value.
2 ½ –3
U5D1
The Symbols and Their MeaningsSymbol Meaning
a > b a is greater than b
a ≥ b a is greater than or equal to b
a < b a is less than b
a ≤ b a is less than or equal to b
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What does it all mean!?
Examples!
Graph each inequality on a number line using or
1.
2.
3.
4.
5x
2x
0x
21x
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properties ws
Solutions to an Inequality
• Remember that the solution to an equation gave us a single, unique result… but for inequalities…
• The solution to an inequality is a range of possibilities.
• Example: The solution of allows every real number that is bigger than 2. So we get to use any possible number we can think of as long as it is greater than 2.2x
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Properties of Inequalities
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What does it all mean!?Examples!
Solve each inequality and graph the solution on a number line.
1.
2.
3.
4.12 x
x312
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64 x
32
x
You Try!
• Solve each inequality and graph the solution on a number line.
1.
2.
3.
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86 x
1211 x
43
x
Independent Practice
U5D1 – ICP
U5D1
GMUnit 5 – Day 2
Standards Addressed Today:
Attend to Precision
Reason Abstractly and Quantitatively
Solve Inequalities Using Algebraic Manipulation
Explain the Multiplication Property by Negative Integers for Inequalities
Concept Review
• Solve each inequality and graph the solution on a number line.
1.
2.
3.
4.
113x
128 x
16
x
357 x
U5D2
Now for the tricky part…
• Consider the inequality 4 < 12
1. Divide both sides by 2. Is the inequality still true?
2. Now divide both sides by –2. Is the inequality still true?
3. Divide by 4.
4. Divide by –4.
5. Now multiply by 2, -2, 3, -3…
U5D2
Solve each inequality
1.
2.
3.
4.
U5D2
162 x
y48
13
x
3
212
w
Challenge!
1.
2.
3.
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4.
5.
6.
)74(22 w )76(226 ww
2
4816
w
xx 921153
3
16212
w
12
8
3
2
w
Describe a situation
… that could be modeled by the inequality
103 x
U5D2
Work with a partner• You are building a patio. You want to cover the patio with Spanish Tile
that costs $5 per square foot. You budget for the tile is $1700. How wide can you make the patio without going over budget?
U5D2
Independent Practice
U5D2 – ICP
U5D2
GM
Unit 5 – Day 3
Standards:
Attend to Precision
Reason Abstractly and Quantitatively
Solve Inequalities Using Algebraic Manipulation
Solve Inequalities Arising From a Context
Concept Review
Solve each equation or inequality
• 13 𝑥 − 10 = 26(3𝑥 − 2)
• −4 − 7𝑥 < 17
U5D3
Inequality Mad Libs!
• Fill in each blank with the appropriate word or number.
The _________ (arithmetic operation) of ________& _______ (#s) is no more than __________ (#).
Write an algebraic inequality and solve.
U5D3
Inequality Mad Libs!
• Fill in each blank with the appropriate word or number.
A ______________ (noun) has _________ (#) times as many _____________ (noun) as ____________ (noun). Together, they have at least ___________ (#).
Write an algebraic inequality and solve.
U5D3
Inequality Mad Libs!
• Fill in each blank with the appropriate word or number.
____________ (proper noun) has ________ (#) bottles of _________ (noun). Together ___________ (first proper noun) and ___________ (second proper noun) have fewer than __________ (#) bottles of _____ (first noun).
Write an algebraic inequality and solve.
U5D3
YOU TRY Inequality Mad Libs
• Write an inequality mad lib on your own.
• Write an algebraic inequality to represent your situation.
• Solve it.
• Then switch Mad Libs with a partner, write the inequality and solve.
Write an algebraic inequality and solve.
U5D3
In Class Practice
U5D3 – ICP
U5D3
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