dec. 6 - absolute value equations
DESCRIPTION
Presentation from in class on December 6, 2011. We talked about how to solve absolute value equations. No additional assignments followed today. Tomorrow we will work on solving absolute value inequalities.TRANSCRIPT
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Absolute ValueThe distance away from 0
0 5-5 10-10
6 6𝑥=−6 𝑥=6
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Absolute ValueThe distance away from 0
0 5-5 10-10
10 10𝑥=−10 𝑥=10
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Absolute ValueWhat two points are 5 away from
0?
0 5-5 10-10
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Solving Absolute Value
|𝑦−1|=3 is 3 units from 0
0 5-5 10-10
𝑦−1=3𝑦−1=−3
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Solving Absolute Value
|3 𝑥|=6To solve (when the absolute value is by itself), split into two equations:• One with a positive 6• The other with a
negative 6
Then solve each individually
3 𝑥=6 3 𝑥=−6
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Solving Absolute Value
|𝑛|+3=5To solve (when the absolute value is by itself), split into two equations:• One with a positive• The other with a
negative
Then solve each individually
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Negative distance?
Thinking about absolute value as the distance from 0, where would we graph p?
TRICK QUESTION! YOU CAN’T HAVE A NEGATIVE DISTANCE!
This creates a no solution
0 5-5 10-10
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Check for Understanding
What’s the solution to
NO SOLUTION, an absolute value makes everything positive, so it cannot
equal a negative number
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Check for Understanding
What’s the solution to
NO SOLUTIONRemember, an absolute value has to equal a positive number
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Guided Practice
|𝑚|+4=19𝑚=15 𝑚=−15
𝑚=15𝑜𝑟𝑚=−15
1. Isolate the Absolute Value
2. Split into two equations
3. Solve each equation
4. CHECK THE ANSWERS!
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1. Isolate the Absolute Value
2. Split into two equations
3. Solve each equation
4. CHECK THE ANSWERS!
Guided Practice
1=|𝑔+1|1=𝑔+1 −1=𝑔+1𝑔=0𝑜𝑟𝑔=−2
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Guided Practice
2|𝑑+3|=8𝑑1. Isolate the Absolute Value
2. Split into two equations
3. Solve each equation
4. CHECK THE ANSWERS!• When you check , you get that the absolute value is
equal to a negative number, therefore, is not a solution
𝑑+3=4𝑑
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Summary
What are the steps to solve an absolute value equation?1. Is the Absolute Value alone?2. Split the Absolute Value into two
equations3. Solve each equation individually4. Check your answers by plugging
them in!
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SummaryOn a half sheet of paper, solve the following to turn in as your ticket out the door. John Doe
D812/6/11
Exit Ticket