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ABSOLUTE VALUE EQUATIONS

Math 8

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Absolute Value

The Absolute Value of a number is it’s distance from Zero

Absolute Value symbols are a grouping symbol, you must complete all operations on the inside and have just a single number BEFORE finding it’s distance from Zero

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Review Absolute Value

 

 

 

 

 

 

 

 

 

 

 

 

 

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Steps for Solving Absolute Value Equations

Remember that two numbers have the same Absolute Value, they are the same distance away from zero. Thus Absolute Value equations have two solutions.

1. Use inverse operations to isolate the expression inside the Absolute Value symbols

2. Take the expression inside the Absolute Value symbols and write two equations

- one is equal to the positive value on the other side of the equation

- the other is equal to the negative value of the number on the other side of the equation

-notice that the solutions are not always opposite numbers of each other

3. Solve each equation separately

4. Check your solutions!!

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Solve each equation

 

 

 

 

 

 

 

 

 

 

Check your solutions!!

 

 

😁

Write two equations

 

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Solve each equation

 

 

 

Write two equations

 

 

 

 

 

 

Check your solutions!!

 

 

😀

 

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Solve each equation

 

 

 

Write two equations

 

 

 

 

 

 

 

 

 

 

Check your solutions!!

😃

 

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Solve each equation

 

 

 

Write two equations

 

 

 

 

 

Check your solutions!!

🙂

Isolate the absolute value expression WITHOUT using Distributive Property

 

 

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Solve each equation

 

Write two equations

 

 

 

 

 

 

Check your solutions!!

🤔

Can the absolute value of something ever equal a negative?

NO!

Special Case:

If the Absolute Value is isolated

but it equals a negative number,

that means there is No Solution.

Absolute Value is always a

positive number.

 

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Solve each equation

 

 

 

Write two equations

 

 

 

 

 

 

Check your solutions!!

😁

Does this equation have No Solution?

 

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Solve each equation

 

 

No Solution

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Solve each equation

 

 

 

 

 

Write two equations

 

 

 

 

 

 

Check your solutions!!

😆

 

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Solve each equation

 

 

 

 

 

Write two equations

 

 

 

 

 

 

 

 

 

 

Check your solutions!!

🥳

 

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