Loading in 5 sec....

Compound Linear InequalitiesPowerPoint Presentation

Compound Linear Inequalities

- 66 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' Compound Linear Inequalities' - hansel

**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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

Identify the Symbol

- Less Than
- Less Than or Equal To
- Greater Than
- Greater Than or Equal To

Identify the Symbol

- Less Than
- Less Than or Equal To
- Greater Than
- Greater Than or Equal To

Identify the Symbol

- Less Than or Equal To
- Greater Than or Equal To
- All Real Numbers
- Not Equal To

Identify the Symbol

- Less Than or Equal To
- Greater Than or Equal To
- All Real Numbers
- Not Equal To

Conjunction

- Mathematical sentences joined by “and”
- Meaning: an intersection

Disjunction

- Mathematical sentences joined by “or”
- Meaning: a union

Which is it?

- All students who have red hair and are boys.
- All students who have brown hair or wear glasses.

x < -3 and x > 1

Where on the number line are both of these statements true?

Solving Conjunctions

- Graph both inequalities.
- Find the intersection. (overlapping portions)
- Write the answer as an inequality.

Conjunction – Case 1

- No overlap and arrows going in the opposite direction
- No solutions

Conjunction – Case 2

- Overlapping and arrows going in the opposite direction
- The solution is between the two numbers.

Conjunction – Case 3

- Overlapping and arrows going in the same direction.
- The solution will be a single greater than/less than inequality.

Solving Disjunctions

- Graph both inequalities.
- Find the union. (Join the two graphs)
- Write the answer as an inequality.

Disjunction – Case 1

- No overlap and arrows going in the opposite direction
- The solution is the original inequalities.

Disjunction – Case 2

- Overlapping and arrows going in the opposite direction
- If every part of the number line is covered at least once, then the solution is all real numbers.

Disjunction – Case 3

- Overlapping and arrows going in the same direction.
- The solution will be a single greater than/less than inequality.

x > 3 or x > 1

- x > 1
- x > 3
- All real numbers
- None of these

x > 3 and x > 1

- x > 1
- x > 3
- All real numbers
- None of these

-6

-3

-5

-2

0

-9

-8

-4

-1

-2x > 4 or x + 8 < 1- Solve each inequality first!
- x < -2 or x < -7
- x < -2

3x – 5 < 1 and x – 5 > -3

- x = 2
- x > 2
- -2 < x < 2
- The empty set
- None of these

-2 < x + 1 < 5

- “x + 1 lies between -2 and 5.”
- Always a conjunction.
- Write as two separate inequalities, then solve as usual.
- x + 1 > -2 and x + 1 < 5

-15 < 3(x – 1) < 12

- x < -4
- -4 < x < 5
- x < 5
- The empty set
- None of these

4x > -12 or x + 6 < 5

- x > -3
- -3 < x < -1
- All real numbers
- The empty set
- None of these

- Section 2.7
- p. 74

Page 74

- 8. 1 < x 7
- 10. All real numbers

Download Presentation

Connecting to Server..