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Solving Equations with Absolute Values

Today’s Lesson. Solving Equations with Absolute Values. Warm- Up Activity. We will warm up today by solving for the absolute values of |4|; |-8|; |1|; |0|; |-6|. The answers are |4| = 4 |-8| = 8 |1| = 1 |0| = 0 |-6| = 6. Whole-Class Skills Lesson.

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Solving Equations with Absolute Values

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  1. Today’s Lesson Solving Equations with Absolute Values

  2. Warm- Up Activity We will warm up today by solving for the absolute values of |4|; |-8|; |1|; |0|; |-6|

  3. The answers are |4| = 4 |-8| = 8 |1| = 1 |0| = 0 |-6| = 6

  4. Whole-Class Skills Lesson Today you will be solving absolute value equations.

  5. Absolute value equations are used to find maximum and minimum values of certain situations.

  6. If an absolute value equation is equal to a negative number, |x +3| = -2 then there is no solution since a distance cannot be negative.

  7. Otherwise, there can be one or two solutions to an absolute value equation.

  8. If an absolute value equation is equal to zero, |x+5| = 0 there is one solution.

  9. If an absolute value equation is equal to a positive rational number greater than 0, |x-3| = 2 there are two solutions.

  10. When an absolute value equation has two solutions, |X + 4| = 3 the absolute value equation needs to be re-written as two equations

  11. : the first is equal to a positive number, and the second is equal to a negative number. |X + 4| = 3 becomes, X + 4 = 3 and X + 4 = -3

  12. Solve this equation. |x + 4| = -2 This equation has no solution since the equation is equal to a negative number.

  13. |x – 5| = 0 Rewrite this as an equation x – 5 = 0 and then solve. The solution to this equation is x = 5.

  14. |x + 6| = 14 Rewrite this as two equations x + 6 = 14 and x + 6 = -14 and then solve each equation. Answers: x = 8; x = -20 (The two solutions are 8 or -20; these are the minimum and maximum values.)

  15. The length of a sleeve on a t-shirt is 18 centimeters and the sleeves can be altered by 2.75 centimeters to be longer or shorter, what are the possible lengths? 15.25 cm or 20.75 cm

  16. How could you write an absolute value equation to represent the minimum and maximum lengths?

  17. Solve this equation. |x + 2| + 4 = 2 There is no solution to this equation.

  18. Solve this equation. |x – 8| – 3 = -3 The solution to this equation is x = 8.

  19. Solve this equation. |x + 2| – 5 = 12 There are two solutions for this equation: x =15 or x = -19.

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