Absolute Value Equations and Inequalities

One-Step Absolute Value Equations

100

l3xl=27

x=-9,9

200

What is lx+5l=10

x=-15, 5

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=6x+4

x=-5/97 (extraneous),x=-3/103

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

l6nl<18

n<3,n>-3

200

lx-2l<8

x<10,x>-6

300

l1+bl<4

b<3, b>-5

400

l10p-4l<34

p<19/5, p>-3

500

l5+b/5l<10

b<25, b>-75

Multi-Step Absolute Value Inequalities

100

lx+2l+2<4

x>-4,x<0

200

2lx+3l>8

x<-7,x>1

300

2lx+2l-1<8

x<2.5, x>-6.5

400

2lx+9l+3>7

x>-7,x<-11

500

3lx/7l>21

x>49,x<-49