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?

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• 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.

x

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LaunchLaunch

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Let’s think about |x|

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• 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.

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|7| = ?

Let’s think about |x|

|7| = 7

xxxx

x then ,0 if then ,0 if

• 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

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Let’s Solve 7 = |x|Since we do not know the value of x, use

the definition for either possibility…

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x = 7 -x = 7

x = -7

So the solution is x = 7 or x = – 7How is this related to our card game?

Let’s Practice1. |x|= 32. |x|= 03. – |x|= 54. | – x|= 75. |x|= – 12

Private think time

Elbow Partner

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Remember Round 4 of the Game?

If the dealer turned over a distance card of positive 5,

Starting cardDistance card

The two solutions are …

-7 - 5 5

212

0 11

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.

-7 - 5 5

212

0

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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 = – 5x = 2

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1. |x – 1|= 02. |-x + 3|= 83. |9 – x|= 24. |2x – 9|= 75. |x – 1|= -¾

Private think time

Elbow Partner

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Team Practice

1. |x – 1|= 02. |-x + 3|= 83. 3|9 – x|= 64. |2x – 9|= 75. |x – 1|= -3/4

1. x = 12. x = -5 or x =

11 3. x = -11 or x = 7 4. x = 1 or x = 8

5. no solution

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Team Practice

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DebriefMake 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

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5

3

12

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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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PracticePractice 5. ___

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Ticket OutSolve

210−x 16