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Check: p. 44 # 5-50(x5), 52

This chapter covers solving and graphing absolute value equations and inequalities. Learn how to solve equations with special cases and compound inequalities. Includes practice problems and a quiz.

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Check: p. 44 # 5-50(x5), 52

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  1. Test Chapter 1 Wednesday Main Events: • Check: p. 44 # 5-50(x5), 52

  2. Algebra 2Warm-up: 1/1/2020 Solve and graph.

  3. Lesson • Quiz 1.1-1.4(was Friday) • Review special cases with compound inequalities. • Classwork Puzzle D-27 • Powerpoint 1.7 with practice

  4. Section 1.7 Objective: Solve and graph absolute value equations and inequalities.

  5. Solve the absolute value equation: -8 0 8 -5 0 5 10 15

  6. Absolute Value Equations and Inequalities To solve absolute value equations, recall that absolute value means “distance away from zero”. Just watchSolve |x + 3| = 5 This means that x + 3 is 5 units away from 0, so there are two possibilities: x + 3 = –5 or x + 3 = 5 –3 –3 –3 –3 or x = –8 x = 2

  7. Solve and graph • Ex 1 Check your answer for extraneous solutions.

  8. EX 2 Isolate the absolute value first: Begin by adding 10 to both sides.

  9. What about inequalities? Example: Solve |x|<3 This means that the distance on number line must be less than or equal to 3. x < 3 and x > –3 –3 < x < 3 -3 0 3

  10. :Solve |x | > 3 This means that the distance on number line is greater than or equal to 3. x > 3 or x < –3 -3 0 3

  11. EX 3 Solve: |x – 3| < 5 “less than”-----And x – 3 < 5 and x – 3 > –5 +3 +3 +3 +3 x < 8 and x > –2 –2 < x < 8

  12. EX 4 Solve: |2x – 8| >4 “great-or than”-----OR 2x – 8 < -4 OR 2x – 8 > 4 +8 +8 +8 +8 2x < 4 2x > 12 x < 2 OR x > 6

  13. Practice 1.7 Solve each of the following: Classwork p. 1010 # 33-53 odd

  14. Homework… p. 55 # 9-11, 28-30, 35, 38, 56, 61

  15. Closure-- • An absolute value equation can have 0, 1, or 2 solutions. Determine the number of solutions for each equation?

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