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Do Now 10/10/19

Do Now 10/10/19. Take out your HW from last night. Text p. 86, #25-30 all Copy HW in your planner. Text p. 91, #4-26 evens, 27 & 29 Quiz Sections 2.5 & 2.6 Tuesday – 10/15 Chapter 2 Test Thursday – 10/17

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Do Now 10/10/19

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  1. Do Now 10/10/19 • Take out your HW from last night. • Text p. 86, #25-30 all • Copy HW in your planner. • Text p. 91, #4-26 evens, 27 & 29 • Quiz Sections 2.5 & 2.6 Tuesday – 10/15 • Chapter 2 Test Thursday – 10/17 • Using your Big Ideas Student Journal, work on Explorations 1 & 2 for Section 2.6. Work with your 6:00 partners. • On the bottom of page 55 in your Student Journal, solve the following absolute value equation. 3|4x + 2| - 7 = 11

  2. HomeworkText p. 86, #25-30 all

  3. HomeworkText p. 86, #25-30 all

  4. HomeworkText p. 86, #25-30 all

  5. Using your Big Ideas Student Journal, complete Explorations 1 & 2 for Section 2.6. • In your notebook, solve the following absolute value equation. 3|4x + 2| - 7 = 11 You can work with your 7:00 partners. x = 1, -2

  6. Learning Goal • SWBAT write, graph, and solve linear, compound, and absolute value inequalities Learning Target • SWBAT solve absolute value inequalities

  7. Section 2.6“Solve Absolute Value Inequalities” ABSOLUTE VALUE INEQUALITY– an inequality that contains an absolute value expression. |x| < 4 means that the distance between x and zero is LESS than 4. |x| > 4 means that the distance between x and zero is GREATER than 4.

  8. < AND ≤Absolute Value Inequalities Flip inequality sign because of negative. Graph |x| < 2 Rewrite x < 2 AND x > -2 Graph x < 2 -2 -1 0 1 2 3 Graph of x > -2 -1 0 1 2 3 -2 Graph of -2 < x < 2 -2 -1 0 1 2 3

  9. GreatOR > OR ≥Absolute Value Inequalities Flip inequality sign because of negative. Graph |x| > 2 Rewrite x > 2 OR x < -2 Graph x > 2 -2 -1 0 1 2 3 Graph of x < -2 -1 0 1 2 3 -2 Graph of x > 2 or x < -2 -2 -1 0 1 2 3

  10. Solving an Absolute Value Inequality The inequality |ax + b| < c where c > 0, will result in a compound AND inequality. -c < ax + b < c The inequality |ax + b| > c where c > 0, will result in a compound OR inequality. ax + b > c or ax + b < -c

  11. Solve an Absolute Value Inequality Solve |x - 5| > 7. Graph your solution |x - 5| > 7 Write original inequality. Rewrite as compound inequality. x - 5 > 7 x - 5 < -7 OR +5 +5 Add 5 to each side. x > 12 OR x < -2 Simplify. Graph of x > 12 or x < -2 -2 0 2 4 6 8 10 12

  12. Solve an Absolute Value Inequality Solve |-4x - 5| +3 < 9. Graph your solution |-4x - 5| +3 < 9 Write original inequality. -3 -3 Subtract 3 from each side. |-4x - 5| < 6 Rewrite as compound inequality. -4x – 5 < 6 -4x - 5 > -6 AND +5 +5 Add 5 to both sides. -4x < 11 -4x > -1 Divide by -4 to each side. AND x > -2.75 AND x < 0.25 Simplify. Graph of -2.75 < x < 0.25 -3 -2 -1 3 0 1 2

  13. On Your Own 1). |d + 4| ≥ 3 2). |9 – 4n| ≤ 5 d ≤ -7 or d ≥ -1 -7 -6 -5 -4 -3 -2 -1 0 1 ≤ n ≤3.5 -1 0 1 5 2 3 4

  14. Solving an Absolute Value Inequality, if possible The inequality |ax + b| < c where c < 0, will result in NO SOLUTION. The inequality |ax + b| > c where c < 0, will result ALL REAL NUMBERS

  15. On Your Own 1). |2c + 4| ≥ -4 2). 3|3 – 2n| ≤ -15 All Real Numbers No Solution

  16. Absolute Deviation • The absolute deviation of a number x from a given value is the absolute value of the difference of x and the given value. |x – given value|= Absolute deviation Find the values of x that satisfy the definition of absolute deviation for the given value of x: Given Value: 5 Absolute deviation: at most 8 |x – given value|= Absolute deviation |x – 5| ≤ 8 x – 5 ≥ -8 x – 5 ≤ 8 x ≥ -3 x ≤ 13

  17. Homework • Text p. 91, #4-26 evens, 27 & 29

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