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Absolute Value Equations November 3, 2014 Page 30-31 in Notes

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Warm-Up – pg. 30 What is absolute value? Solve: – |-2| – |3|

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Objective [6E*] solve absolute value linear equations

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Solving Absolute Value Equations Title – page 31

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Essential Question How do I solve absolute value equations algebraically?

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Steps: Isolate the absolute value expression. Set up 2 linear equations and solve. – Positive Case or Negative Case Check both answers back in the original equation. (They may not work!)

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Example 1 |x + 2| = 7 x + 2 = 7or x + 2 = -7 Already isolated -2 -2 x = -9 -2 -2 x = 5or |x + 2| = 7 |(5) + 2| = 7 |7| = 7 7 = 7 |x + 2| = 7 |(-9) + 2| = 7 |-7| = 7 7 = 7 Check: {-9, 5}

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Example 2 |3x – 6| – 5 = -7 +5 +5 |3x – 6| = -2 3x – 6 = -2 or 3x – 6 = 2 +6 +6 3x = 4 x=4/3or +6 +6 3x = 8 x = 8/3 Check: |3(4/3) – 6| – 5 = -7 |4 - 6| = -2 |-2| = -2 2 = -2 |3(8/3) – 6| – 5 = -7 |8 - 6| = -2 |2| = -2 2 = -2 No Solution

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On Your Own #1 (Left Side) 5|y – 2| = 30 I’ll even get you started! Divide both sides of the equal sign by 5… |y – 2|= 6

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Answer…{-4, 8} Were you correct?

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On Your Own #2 (Left Side) 10 – 10|-8k + 4| = 10 I’ll even get you started! Subtract 10 from both sides, then divide by -10.

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Answer…{1/2} There is only one solution! Were you correct?

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Activity Each pair will receive an equation to solve. Find the correct solution cards. Find the other pair that has the same solutions as you and check them with me. Trade cards with another pair (not the ones you just matched with) and repeat.

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Absolute Value Equations Homework 1.{#, #} 5. 2. or {#} 6. 3. or No Solution7. 4. 8. 1. Write problem and show work

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Homework Problems – Due Tuesday 1.|3x – 1| + 5 = 3 2.5|c – 2| = 30 3.|-2x – 1| = 11 4.|p + 8| – 5 = 2 5.-8|3 – 8k| = 40 6.10|7x + 3| = 0

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Reflection Exit Ticket: Explain how an absolute value equation can have 2 solutions.

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