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# Friday, september 27, 2012

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### Friday, september 27, 2012

1. 1. Friday, September 27, 2013 Today: Make-Up Tests Now Warm-Up Absolute Value Equations Khan Academy Due Sunday: 7:00 pm Class work:
2. 2. Warm-Up (5); fr. Test Version 1 1) .3x + .3 = .6x + .7 - .5x A) .32 B) 15 C) 2 D) .4 E) None Version 2 Version 3 9) The first stage of a rocket burns 28 seconds longer than the second stage. If the total burning time for both stages is 182 seconds, how many seconds does the first stage burn for? A) 124 B) 77 C) 98 D) 90 E) 105
3. 3. Absolute Value 0 5-5 10-10 10 10
4. 4. Absolute Value 0 5-5 10-10
5. 5. Solving Absolute Value Equations To solve (when the absolute value is by itself), split into two equations: • One with a positive 3x • The other with the opposite of 3x = 6 Then solve each individually What are x = 2; x = -2 Because the |x|could be positive or negative, (why)we must solve for both possibilities.
6. 6. Check for Understanding What is the solution to |3x + 1| = - 5 There is no solution. The result of an absolute equation can never be negative. But what about the second equation that we write using a negative sign? The difference is: The original equation is always a positive. For example, |3x + 1| = 5 If the original absolute value equation equals a negative number, there is no solution.
7. 7. Guided Practice Ex.1: 3|x - 1| + 1 = 10 For the Positive Value: 1. Goal: Isolate the absolute value a. Subtract 1 b. Divide by 3 c. add 1. x = 4 3|x - 1| + 1 = 10 - 1 - 1 3|x - 1| = 9 |x - 1| = 3 x = 4 3|x - 1| + 1 = 10 - 1 - 1 3|x - 1| = 9 -x + 1 = 3 -x = 2; x = -2 For the Negative Value: 1. Goal: Take the opposite of the absolute value 2. a. Subtract 1 b. Divide by 3 c. Take the opposite of the ab. value d. add 1; x = -2 Plug in and check each value!!!!
8. 8. Summary What are the steps to solve an absolute value equation? 1. Is the Absolute Value alone (isolated) on one side? 2. Split the Absolute Value into two equations 3. One equation takes the absolute value, one takes the opposite of the absolute value 4. Solve each equation individually 5. Check your answers by plugging them in!
9. 9. Absolute Value 4. |x + 6| + 12 = 18 Solve for the positive first b. Subtract 6 from each side. x = ? Goal: Get the absolute value by itself on the left side. a. Subtract 12 from each side 0
10. 10. Warm-Up Solve for the negative next Goal: Get the absolute value by itself on the left side before taking the opposite: a. Subtract 12 from each side b. We have |x + 6|= 6; Now we can change the equation to: -|x + 6|, or -x - 6 = 6; -x = 12; x = -12 The solutions are x = 0, or x = -12 Absolute Value e. Plug in each value. Are both -4 & -8 solutions?
11. 11. Absolute Value: Last Problem The highest elevation in North America is Mt. McKinley, which is 20,320 feet above sea level. The lowest elevation is Death Valley, which is 282 feet below sea level. What is the distance from the top of Mt. McKinley to the bottom of Death Valley?
12. 12. Class Work: Handout: Please use separate page for NUMBERED scratch paper.