Solve Absolute Value Equations © Evergreen Public Schools 2010

I can write and solve an absolute value equation from a given situation with one variable. What do you think is the solution to | x + 1| = 5? What do you think is the solution to | x + 1| = 5? 2 Learning Target

Think about the card games we played yesterday. Make a list of numbers that are not changed by the absolute value bars. Make another list of numbers that are changed by the absolute value bars. Write down a general rule that describes what absolute value does to any given number. 3 LaunchLaunch

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Let’s think about | x | 5 Share with your partner how you answered the questions. I will be asking you to tell us what your partner wrote.

Think about the card games we played yesterday. If x is non-negative then just write it without the bars. 6 |7| = ? Let’s think about | x | |7| = 7

If x is non-negative then just write it without the bars. If x is negative then make it the opposite value. 7 |-4| = ? Let’s think about | x | |-4| = 4

Think about the card game yesterday If we knew the answer was 7, what card could give us that answer? A positive 7 A negative 7 8

Let’s Solve 7 = | x | Since we do not know the value of x, use the definition for either possibility… 9 x = 7 -x = 7 x = -7 So the solution is x = 7 or x = – 7 How is this related to our card game?

Let’s Practice 1.| x |= 3 2.| x |= 0 3.– | x |= 5 4.| – x |= 7 5.| x |= – 12 Private think time Elbow Partner 10

Remember Round 4 of the Game? If the dealer turned over a distance card of positive 5, Starting card Distance card The two solutions are … and the caller turned over a negative of positive 7

Remember Round 4 of the Game? So, you can add 2 to -7 and be 5 units from zero, and you can add 12 to -7 and be 5 units from zero

Let’s Solve: 5 = | x – 7| Since we do not know the value of x – 7, use the definition for either possibility… x – 7 = 5 x = 12 So the solution is x = 12 or x = 2 The same solution as the previous slide, but a little faster. x – 7 = – 5 x = 2 13

1.| x – 1|= 0 2.|- x + 3|= 8 3.|9 – x |= 2 4.|2 x – 9|= 7 5.| x – 1|= -¾ Private think time Elbow Partner 14

1.| x – 1|= 0 2.|- x + 3|= 8 3.3|9 – x |= 6 4.|2 x – 9|= 7 5.| x – 1|= -3/4 1. x = 1 2. x = -5 or x = x = -11 or x = 7 4. x = 1 or x = 8 5. no solution 15

©Evergreen Public Schools Debrief Make a mini poster to explain your understanding of solving absolute value equations. Write an absolute value equation. Show how the following are related number line equation solution explanation

©Evergreen Public Schools Learning Target Did you hit the target? I can solve inequalities in one variable. Rate your understanding of the target from 1 to 5. 5 is a bullseye!

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