Solving & Graphing Linear Inequalities & Compound ... · 07/10/2018 · Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook 24 October

Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook

1

October 25, 2017

Sep 711:06 PM

Solving Linear

& Graphing

Inequalities


2

October 25, 2017

Sep 131:02 PM

Open circle on the graph means that the

inequality will be greater than or less than.

Closed circle on the graph means that the

inequality will be “greater than or equal to”

OR “less equal than or equal”.

> or


3

October 25, 2017

Sep 131:08 PM

If the direction of the GRAPH is pointed to the LEFT, then inequality is "less than" or "less than or equal to".

If the direction of the GRAPH is pointed to the RIGHT, then inequality is "greater than" or "greater than or equal to".

10 2 3 4 5 6 7 8 9 1012345678910

10 2 3 4 5 6 7 8 9 1012345678910


4

October 25, 2017

Oct 2111:03 AM

>greater thanside of any inequality less thanside of any inequality>greater than

side of any inequality

less thanside of any inequality

OR


5

October 25, 2017

Sep 1312:58 PM

EXAMPLE 1

Given the graph, below :

012345 1 2 3 4 5 6 767

orb)

SOLUTION

b) Write an inequality to express the graph on the number line, use x as your variable.

a) Write a statement in words to express the graph on the number.

a) All numbers less than 2.–


6

October 25, 2017

Sep 131:23 PM

EXAMPLE 2

012345 1 2 3 4 5 6 767

SOLUTION

orb)

Given the graph, below :

b) Write an inequality to express the graph on the number line, use x as your variable.

a) Write a statement in words to express the graph on the number.

a) All numbers greater than or equal to 5.–


7

October 25, 2017

Oct 2111:13 AM

SOLUTION

Solve the inequality, then graph the solution set on a number line.

EXAMPLE 3


8

October 25, 2017

Oct 2111:20 AM

012345 1 2 3 4 5 6 767

+ 7 + 7

6 6

x 3x is greater than or equal to 3


9

October 25, 2017

Oct 2111:25 AM

EXAMPLE 4


SOLUTION

23


10

October 25, 2017

Oct 2111:30 AM

23


11

October 25, 2017

Oct 2111:37 AM

EXAMPLE 5


SOLUTION

Eliminate the fractions by multiplying the entire equation by the least common denominator.

Least common denominator of 4, 14, and 7 is 28.

28( )


12

October 25, 2017

Oct 2111:41 AM

28( )

28 28 28– –

28 28 28– – 7 2 4


13

October 25, 2017

Oct 2112:01 PM

+ 4x4x+

+21 +21


14

October 25, 2017

Oct 2112:03 PM

Keep the direction of the inequality symbol the same, we divided by a positive number. It does matter that the solution is negative number.

012345 1 2 3 4 5 6 767


15

October 25, 2017

Oct 211:28 PM

EXAMPLE 6


SOLUTION

1

+ x + x


16

October 25, 2017

Sep 710:14 PM

The inequality is TRUE.

ALL REAL NUMBERS

012345 1 2 3 4 5 6 767


17

October 25, 2017

Oct 211:35 PM

EXAMPLE 7


SOLUTION

– 6x – 6x


18

October 25, 2017

Oct 211:39 PM

The inequality is FALSE.

012345 1 2 3 4 5 6 767

NO SOLUTION


19

October 25, 2017

Sep 1312:44 PM

COMPOUND

INEQUALITIES


20

October 25, 2017

Oct 211:42 PM

EXAMPLE 8


SOLUTION


21

October 25, 2017

Oct 211:44 PM


22

October 25, 2017

Sep 710:33 PM

AND

How to graph a compound inequality ?

Rewrite as 2 separate inequalities.


23

October 25, 2017

Oct 211:40 PM

012345 1 2 3 4 5 6 767

Graph each inequality separately.


24

October 25, 2017

Sep 132:08 PM

012345 1 2 3 4 5 6 767

012345 1 2 3 4 5 6 767

When graphing compound inequalities with an AND, we will take the INTERSECTION of the graphs.


25

October 25, 2017

Oct 212:18 PM

EXAMPLE 9


SOLUTION

4x + 3 6x >11– OR – –4 (3x 5) 12

4x + 3 6x >11– OR – –4 1(3x 5) 12

2x + 3


26

October 25, 2017

Oct 211:55 PM

2x 8– 2– 2– >

OR –9 3x 12

– 3x 3x

Attachments

notebook.galleryitem

imsmanifest.xml

ADL SCORM CAM 1.3 metadata.xml

metadata.xml

URI http://www.adlnet.org/metadata/MDO_01 LOMv1.0 SCORM_CAM_v1.3 URI http://tempuri.org/randomid?id=FAD1A5B6-03DC-4F60-BE37-5517FB536C49 application/x-smarttech-galleryitem;x-original-type=image/xml+svg LOMv1.0 browser LOMv1.0 x-smarttech-notebook ms-windows:9.5;macos:9.5;unix:9.5 LOMv1.0 no LOMv1.0 yes 2013-09-07T19:39:46 1.0 LOMv1.0 final

page0.svg

0 -1 -2 -3 -4 -5 -6 1 2 3 4 5 6 7 8 -7

preview.png

SMART Notebook

Page 1Page 2Page 3Page 4Page 5Page 6Page 7Page 8Page 9Page 10Page 11Page 12Page 13Page 14Page 15Page 16Page 17Page 18Page 19Page 20Page 21Page 22Page 23Page 24Page 25Page 26Attachments Page 1

Documents

Solving & Graphing Linear Inequalities & Compound ... · 07/10/2018 · Solving & Graphing Linear Inequalities & Compound Inequalities[InClass Version]Algebra 1.notebook 24 October