Download presentation

Presentation is loading. Please wait.

1
**Solving Addition and Subtraction Inequalities**

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 ‹ ‹ ‹ 3 2 › -4 2 – 3 › -4 – 3 -1 › 7

3
Example 1 Solve x + 14 ≥ 5 x + 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
**X is greater than or equal to -9**

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 › y › y Since 16 › y is the same as y ‹ 16, the solution is {y l y ‹ 16}. ` 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 }

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

Similar presentations

Presentation is loading. Please wait....

OK

Chapter 4 Inequalities < Less Than > Greater Than.

Chapter 4 Inequalities < Less Than > Greater Than.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on bluetooth architecture Ppt on disk formatting tools Ppt on 60 years of indian parliamentary Ppt on teamviewer 9 Ppt on liberal education Ppt on solar system and earth Ias 33 earnings per share ppt online Job based pay ppt online Ppt on production operation management Attractive backgrounds for ppt on social media