1 / 15

Warm-up – pick up handout up front

Learn to solve linear inequalities, recognize solutions using interval notation, and graph solution sets. Explore types of solutions and reasoning behind unique cases. Practice examples included.

dkoester
Download Presentation

Warm-up – pick up handout up front

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. Answers: • x=0, x=1/10, x= -1/10 Warm-up – pick up handout up front 1. Solve for x 2. 2. Solve by factoring. 1000x3-10x HW 1.7A (2-14 evens, 21-24, 39-47)

  2. HW 1.6B (31-39 all)HW 1.6C (61-75 odds)

  3. Lesson 1.7A Solving linear inequalities and the types of notation Objective: To be able to use interval notation when solving linear inequalities, recognize inequalities with no solution or all real numbers as a solution. The set of all solutions is called the solution set of the inequality. Set-builder notation and a new notation called interval notation, are used to represent solution sets. (See Handout!)

  4. Interval Notation: See Handout

  5. Example 1: (-1,4] Graph and write the solution in set-builder notation. ( ] -1 0 4 ) -4 0 Interval Notation Set Builder Notation (-1,4] = {x -1 < x ≤ 4} The answer is read x such that -1 is less than x which is less than or equal to 4. You Try: (-∞, -4) (-∞, -4)= { x x < -4}

  6. Graphing intervals on a number line! Example 2: Graph each interval on a number line. ( ] 2 3 {x 2 < x < 3} (2,3] Write answer using set builder notation.

  7. You try: Graph and write in set builder notation. [ ) 1 6 ( ] -3 7 [1,6) {x 1 < x < 6} {x -3 < x < 7} (-3,7]

  8. Example 3: Solve and graph this linear inequality. ) -3 0 -2x - 4 > x + 5 Remember to switch the sign when you multiply or divide by a negative. x < -3

  9. You Try!! ) 4 3x+1 > 7x – 15 Use interval notation to express the solution set. Graph the solution. Answer: (-∞, 4)

  10. Inequalities with Unusual Solution Sets Some inequalities have no solution. Example 4: x > x+1 There is no number that is greater than itself plus one. The solution set is an empty set ( this is a zero with a slash through it)

  11. Notes Continued: Like wise some inequalities are true for all real numbers such as: Example 5: x<x+1. Every real number is less than itself plus 1. The solution set is { x x is a real number} Interval notation, or all real numbers.

  12. Notes Continued: When solving an inequality with no solution, the variable is eliminated and there will be a false solution such as 0 > 1. When solving an inequality that is all real numbers, the variable is eliminated and there will be a true solution such as 0 < 1.

  13. Example 6:Solving a linear inequality for a solution set. A. 2 (x + 4) > 2x + 3 B. x + 7 < x – 2 solution: 7 < -2 solution: 8 > 3 The inequality 8>3 is true for all values of x. The solution set is {x x is a real number} or The inequality 7 < -2 is false for all values of x. The solution set is

  14. You try: 3(x + 1) > 3x + 2 3x + 3 > 3x + 2 3 > 2 The solution set is all real numbers. (-∞,∞) Summary: Describe the ways in which solving a linear inequality is different from solving a linear equation.

More Related