1 / 10

Chapter 12 Section 2

Chapter 12 Section 2. Solving Addition and Subtraction Inequalities. Addition and Subtraction Properties for Inequalities. Words: For any inequality, if the same quantity is added or subtracted to each side, the resulting inequality is true. Symbols: For all numbers a, b, and c,

belle
Download Presentation

Chapter 12 Section 2

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. Chapter 12 Section 2 Solving Addition and Subtraction Inequalities

  2. Addition and Subtraction Properties for Inequalities Words: For any inequality, if the same quantity is added or subtracted to each side, the resulting inequality is true. Symbols: For all numbers a, b, and c, 1. If a › b, then a + c › b + c and a – c › b – c. 2. If a ‹ b, then a +c ‹ b +c and a – c ‹ b – c. Numbers: -5 ‹ 1 -5 + 2 ‹ 1 + 2 -3 ‹ 3 2 › -4 2 – 3 › -4 – 3 -1 › 7

  3. Example 1 Solve x + 14 ≥ 5 x + 14 ≥ 5 - 14 -14 x ≥ -9 The solution is all numbers greater than or equal to -9 . To check your answer substitute a number less than -9 and greater into the inequality.

  4. Your Turn Solve the inequality. Check your Solution. x + 2 ‹ 7 All numbers less than 5

  5. Your Turn Solve the inequality. Check your Solution. x - 6 ≥ 12 All numbers greater than or equal to 18

  6. Set-builder Notation A more concise way to express the solution to an inequality is to use set-builder notation. The solution in example 1 in set-builder notation is {x l x ≥ -9}. {x l x ≥ -9} The set of all numbers x Such that X is greater than or equal to -9

  7. In lesson 12-1, you learned that you can show the solution to an inequality on a line graph. The solution, {x l x ≥ -9}, is shown below. -12 -11 -10 -9 -8 -7

  8. Example 2 Solve 7y + 4 › 8y -12. Graph the solution. 7y + 4 › 8y -12 7y – 7y + 4 › 8y – 7y -12 4 + 12 › y-12 + 12 16 › y Since 16 › y is the same as y ‹ 16, the solution is {y l y ‹ 16}. ` 14 15 16 17 18 The graph of the solution has a circle at 16, since 16 is not included. The arrow points to the left.

  9. Your Turn Solve each inequality. Graph the solution. 5y - 3 › 6y - 9 {y l y ‹ 6 } 4 5 6 7 8

  10. Your Turn Solve each inequality. Graph the solution. 3r + 7 ≤ 2r + 4 {y l y ≤ -3 } -5-4 -3 -2 -1

More Related