1 / 22

Write out the compound inequalities. x is at most -4 or at least 1

5.5. Warm-Up. Write out the compound inequalities. x is at most -4 or at least 1 x is less than 7 and greater than or equal to 0 Solve the inequalities. -11 < -3x – 2 < 1 4. -2x – 3 > 5 or 3x + 2 > -1. x < -4 or x > 1. 0 < x < 7. x < -4 or x > -1. -1 < x < 3.

beatricew
Télécharger la présentation

Write out the compound inequalities. x is at most -4 or at least 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 5.5 Warm-Up • Write out the compound inequalities. • x is at most -4 or at least 1 • x is less than 7 and greater than or equal to 0 • Solve the inequalities. • -11 < -3x – 2 < 1 4. -2x – 3 > 5 or 3x + 2 > -1 x < -4 or x > 1 0 < x < 7 x < -4 or x > -1 -1 < x < 3

  2. Solving Absolute Value Equations and Inequalities Objectives: Solve absolute value equations Solve absolute value inequalities Vocabulary: absolute value 5.5

  3. Absolute Value (|x|) the distance a number is away from the origin on a number line The distance away from zero is less than 3 in both the positive and negative direction.

  4. Simplify these expression: 0 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 5.5 Absolute value – the distance a number is away from the origin on a number line |-5| |7| |-4 – 7| |2(3 – 8)| 5 7 11 10

  5. Solving Absolute Value Equations and Inequalities Solve this equation: 5.5 x = 4 x = 4 and x = -4

  6. Solving Absolute Value Equations and Inequalities Solve this equation: 5.5 x = 7 x = 7 and x = -7

  7. Solving Absolute Value Equations and Inequalities Solve this equation: 5.5 x = -2 No solution! An absolute value must always be positive!

  8. Solving Absolute Value Equations and Inequalities Solve this equation: 5.5 • Solving Absolute Equations: • Isolate the absolute value. • Break it into 2 problems – one positive and the other negative. • Solve both equations. • Check both answers. x + 4 = 12 x = 8 and x = -16

  9. Solving Absolute Value Equations and Inequalities Solve this equation: 5.5 • Solving Absolute Equations: • Isolate the absolute value. • Break it into 2 problems – one positive and the other negative. • Solve both equations. • Check both answers. |3x – 3| = 6 x = 3 and x = -1

  10. Solving Absolute Value Equations and Inequalities Solve this equation: 5.5 • Solving Absolute Equations: • Isolate the absolute value. • Break it into 2 problems – one positive and the other negative. • Solve both equations. • Check both answers. |x – 2| + 4 = 8 x = 6 and x = -2

  11. Solve these equations: Example 1 Solving an Absolute Value Equation a.)|6x – 3|= 15 b.)|2x – 8|+ 2 = -22 No solution; an absolute value can never give a negative answer! x = 3 and x = -2 • Solving Absolute Equations: • Isolate the absolute value. • Break it into 2 problems – one positive and the other negative. • Solve both equations. • Check both answers.

  12. Solving an Absolute Value Inequality Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x < -c or x > c “or” REMEMBER: <, <: less thAND >, >: greatOR • Solving Absolute Inequalities: • Isolate the absolute value. • Set up the problem appropriately: “and” or “or.” • Solve the inequalities. • Check both answers. The setup does not need absolute value symbols!

  13. Solve and graph the inequality: Watch Solving an Absolute Value Inequality |x|< 5 • Solving Absolute Inequalities: • Isolate the absolute value. • Set up the problem appropriately: “and” or “or.” • Solve the inequalities. • Check both answers. -5 < x < 5 Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x < -c or x > c “or” <, <: Less thAND >, >: GreatOR

  14. Solve and graph the inequalities: Example 2 Solving an Absolute Value Inequality a.) |4x – 6| < 22 b.)|3x – 9| > 18 • Solving Absolute Inequalities: • Isolate the absolute value. • Set up the problem appropriately: “and” or “or.” • Solve the inequalities. • Check both answers. -4 < x < 7 x < -3 or x > 9 Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x < -c or x > c “or” <, <: Less thAND >, >: GreatOR

  15. Solve and graph the inequality: Example 3 Solving an Absolute Value Inequality |10 – 4x|≤ 2 • Solving Absolute Inequalities: • Isolate the absolute value. • Set up the problem appropriately: “and” or “or.” • Solve the inequalities. • Check both answers. 3 > x > 2 2 < x < 3 Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x < -c or x > c “or” <, <: Less thAND >, >: GreatOR

  16. Solve and graph the inequality: Example 4 Solving an Absolute Value Inequality |x + 2| – 5 ≥ 8 • Solving Absolute Inequalities: • Isolate the absolute value. • Set up the problem appropriately: “and” or “or.” • Solve the inequalities. • Check both answers. x < -15 or x > 11 Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x < -c or x > c “or” <, <: Less thAND >, >: GreatOR

  17. Solve and graph the inequality: Example 5 Solving an Absolute Value Inequality |3x + 2| – 1 ≥ 10 • Solving Absolute Inequalities: • Isolate the absolute value. • Set up the problem appropriately: “and” or “or.” • Solve the inequalities. • Check both answers. x < -13/3 or x > 3 Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x < -c or x > c “or” <, <: Less thAND >, >: GreatOR

  18. Solve and graph the inequality: Example 6 Solving an Absolute Value Inequality |2x + 5| – 1 < 6 • Solving Absolute Inequalities: • Isolate the absolute value. • Set up the problem appropriately: “and” or “or.” • Solve the inequalities. • Check both answers. -6 < x < 1 Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x < -c or x > c “or” <, <: Less thAND >, >: GreatOR

  19. Example 8 Apply Absolute Value Inequalities RAINFALL The average annual rainfall in California for the last 100 years is 23 inches. However, the annual rainfall can differ by 10 inches from the 100 year average. What is the range of annual rainfall for California?

  20. Example 9 A thermostat inside Macy’s house keeps the temperature within 3 degrees of the set temperature point. If the thermostat is set at 72 degrees Fahrenheit, what is the range of temperatures in the house? A. {x | 70 ≤ x ≤ 74} B. {x | 68 ≤ x ≤ 72} C. {x | 68 ≤ x ≤ 74} D. {x | 69 ≤ x ≤ 75}

  21. Algebra 1 Connect Four Practice: • Each student will be responsible for working out every problem. • If it is your turn and you get the problem correct, put your initials in any of the bottom squares (like dropping a chip in the Connect Four board). • If it is your turn and you get the problem wrong, your partner will get a chance to “steal” your turn. • Can’t agree on an answer? Raise your hand! Do not argue/shout/get worked up. • Connect four in a row to win the game! Show your work for each problem on a separate sheet of paper! Number the problems. This will be collected for points!

  22. Algebra 1 Assignment due tomorrow: 5.5 Homework Worksheet

More Related