Download presentation

Presentation is loading. Please wait.

1
**Compound Inequalities**

Section 3.4 Compound Inequalities

2
**Objectives Basic Concepts Symbolic Solutions and Number Lines**

Numerical and Graphical Solutions Interval Notation

3
Basic Concepts A compound inequality consists of two inequalities joined by the words and or or. 2x > –5 and 2x ≤ 8 x + 3 ≥ 4 or x – 2 < –6

4
Example Determine whether the given x-values are solutions to the compound inequalities. x + 2 < 7 and 2x – 3 > 3 x = 4, –4 Solution x + 2 < 7 and 2x – 3 > 3 Substitute 4 into the given compound inequality < 7 and 2(4) – 3 > 3 6 < 7 and 5 > 3 True and True Both inequalities are true, so 4 is a solution.

5
Example (cont) Determine whether the given x-values are solutions to the compound inequalities. x + 2 < 7 and 2x – 3 > 3 x = 4, –4 Solution x + 2 < 7 and 2x – 3 > 3 Substitute –4 into the given compound inequality. –4 + 2 < 7 and 2(–4) – 3 > 3 – 2 < 7 and –11 > 3 True and False To be a solution both inequalities must be true, so –4 is not a solution.

6
**Symbolic Solutions and Number Lines**

We can use a number line to graph solutions to compound inequalities, such as x < 7 and x > –3. x < 7 x > –3 x < 7 and x > –3 Note: A bracket, either [ or ] or a closed circle is used when an inequality contains ≤ or ≥. A parenthesis, either ( or ), or an open circle is used when an inequality contains < or >.

7
Example Solve 3x + 6 > 12 and 5 – x < 11 . Graph the solution. Solution 3x + 6 > 12 and 5 – x < 11

8
Example Solve each inequality. Graph each solution set. Write the solution in set-builder notation. a. b. c. Solution a. b.

9
Example (cont) c.

10
Example Solve x + 3 < –2 or x + 3 > 2 Solution x + 3 < –2 or x + 3 > 2 x < –5 or x > –1

12
Example Write each expression in interval notation. a. –3 ≤ x < 7 b. x ≥ 4 c. x < –3 or x ≥ 5 d. {x|x > 0 and x ≤ 5} e. {x|x ≤ 2 or x ≥ 5}

13
Example Solve 2x + 3 ≤ –3 or 2x + 3 ≥ 5 Solution 2x + 3 ≤ –3 or 2x + 3 ≥ 5 2x ≤ –6 or 2x ≥ 2 x ≤ –3 or x ≥ 1 The solution set may be written as (, 3] [1, )

Similar presentations

OK

2-1 © 2008 Pearson Prentice Hall. All rights reserved Chapter 2 Equations, Inequalities, and Problem Solving Active Learning Questions.

2-1 © 2008 Pearson Prentice Hall. All rights reserved Chapter 2 Equations, Inequalities, and Problem Solving Active Learning Questions.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on political parties and electoral process Ppt on pin diode switch Ppt on self awareness activities Free download ppt on cybercrime in india Ppt on education schemes in india Ppt on social media advertising Ppt on preparation of alkanes Ppt on global warming for class 9 free download Ppt on multivariate statistical analysis Ppt on sports day japan