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Do Now

Do Now. Solve a compound inequality with “or”, Graph. 2x + 3 < 9 or 3x – 6 > 12 Solve a compound inequality with “and”, Graph.   -6 < 3n + 9 < 21. Simplify:. Evaluate:. If x = -6. If a = 2. Objective: To solve absolute value equations. Using Absolute Value in Real Life.

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Do Now

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  1. Do Now Solve a compound inequality with “or”, Graph. 2x + 3 < 9 or 3x – 6 > 12 Solve a compound inequality with “and”, Graph.   -6 < 3n + 9 < 21

  2. Simplify:

  3. Evaluate: If x = -6 If a = 2

  4. Objective: To solve absolute value equations

  5. Using Absolute Value in Real Life The graph shows the position of a diver relative to sea level. Use absolute value to find the diver’s distance from the surface.

  6. When do we use absolute value Determine the difference in altitude between: Death Valley (86 meters below sea level) -86 Mt Everest (8,840 meters above sea level).+ 8840 -86-8840= -8826

  7. Absolute Value Absolute Value- of a number is the distance between the number and zero on a number line ** No such thing as a negative distance **

  8. Solving absolute value equations • If |x| = 5, then what values of x would make the equation true?

  9. If |x| = 5, then is |5| = 5 true? • If |x| = 5, then is |-5|=5 true?

  10. x = -5 x = 5

  11. Practice • = 3 = - 4 =2

  12. Solving absolute value equations ? • |x - 2| = 5 What goes in the box to make the equation true? 5 or -5

  13. Solving absolute value equations ? • |x - 2| = 5 Now lets remove the box and set what’s behind it equal to 5 and -5

  14. Solving absolute value equations • |x - 2| = 5 Now lets remove the box and set what’s behind it equal to 5 and -5

  15. Solving Absolute Value Equations x – 2 = 5 x – 2 = -5 x = 7 x = -3 Or

  16. Ex: Solve 6x-3 = 15 6x-3 = 15 or 6x-3 = -15 6x = 18 or 6x = -12 x = 3 or x = -2 * Plug in answers to check your solutions!

  17. On an index card make up an absolute value equation for your partner to solve. Trade cards.

  18. Solve Two steps Absolute Value Equations • Steps • 1) Isolate the absolute value first • 2) Write it as two equations • 3)solve each equation • 4)test both solutions

  19. Ex: Solve 2x + 7 -3 = 8 Get the abs. value part by itself first! 2x+7 = 11 Now split into 2 parts. 2x+7 = 11 or 2x+7 = -11 2x = 4 or 2x = -18 x = 2 or x = -9 Check the solutions.

  20. 6|5x + 2| = 312 • Isolate the absolute value expression by dividing by 6. 6|5x + 2| = 312 |5x + 2| = 52 • Set up two equations to solve. • 5x + 2 = 52 5x + 2 = -52 • 5x = 50 5x = -54 • x = 10 or x = -10.8 • Check:6|5x + 2| = 312 6|5x + 2| = 312 • 6|5(10)+2| = 312 6|5(-10.8)+ 2| = 312 • 6|52| = 312 6|-52| = 312 • 312 = 312 312 = 312

  21. 3|x + 2| -7 = 14 • Isolate the absolute value expression by adding 7 and dividing by 3. 3|x + 2| -7 = 14 3|x + 2| = 21 |x + 2| = 7 • Set up two equations to solve. • x + 2 = 7x + 2 = -7 • x = 5 or x = -9 • Check:3|x + 2| - 7 = 14 3|x + 2| -7 = 14 • 3|5 + 2| - 7 = 14 3|-9+ 2| -7 = 14 3|7| - 7 = 14 3|-7| -7 = 14 • 21 - 7 = 14 21 - 7 = 14 • 14 = 14 14 = 14

  22. On your own

  23. Exit Ticket • In your own words explain what is the difference between solving regular equations and absolute value equations?

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