Absolute Value Equations and Inequalities and Graphs

One-Step Absolute Value Equations

100

l3xl=27

x=-9,9

200

BONUS QUESTION: What is Ms. A's first name?

Aftyn

300

l4x+22l=30

x=-13, 8

400

l8p/3l=4

p=-3/2,3/2

500

l17d/4l=127

x=-508/7,508/7

Multi-Step Absolute Value Equations

100

lv+8l-5=2

v=-15,-1

200

l5xl+5=45

x=-8,8

300

6l1-5xl-9=57

x=-2, 12/5

400

l8x+4l/2=16

x=-9/2,7/2

500

2l100x+4l+6=4

No Solution

Absolute Value Graphs

100

How has the graph of y=lx+3l shifted from the origin?

To the left 3 units

200

How does the graph of y=2|x| differ from y=|x| ?

The a value is greater, so it is more narrow.

300

Graph the function: y=|x-2|

Opens up, shifted right 2.

400

Graph the function: y=-2|x+1|+5

Opens down, vertex at (-1,5). Slopes -2 and 2.

500

Graph the function: y=3|x-4|-4

Opens up, vertex at (4,-4). Slopes 3 and -3

One-Step Absolute Value Inequalities

100

BONUS QUESTION: What day of the year is "pi day"?

March 14(3/14)

200

lx-2l<8

-6<x<10

300

l1+bl+5<4

No Solution

400

l10p-4l<34

-3<p<19/5

500

l5+b/5l<10

-75<b<25

Multi-Step Absolute Value Inequalities

100

lx+2l+2<4

-4<x<0

200

2lx+3l>-8

All Real Numbers

300

2lx+2l-1<8

-6.5<x<2.5

400

2lx+9l+3>7

x>-7 or x<-11

500

3lx/7l>21

x>49 or x<-49