Absolute Value Equations and Inequalities

One-Step Absolute Value Equations

100

l3xl=27

x=-9,9

200

 lx+5l=10

x=-15, 5

300

l4x+22l=30

x=-13, 8

400

l8 + p/3l=4

p=-36, -12

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

l8x + 4l=|x - 8|

x=-12/7, 4/9

400

Find ALL solutions:

lx + 9l=6x - 10

x = 19/5

500

2l100x+4l+6=6x+4

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

Absolute Value Inequalities

100

l6nl<18

n<3,n>-3

200

2lx-2l<8

x<6,x>-6

300

l1+bl + 3 < 7

b<3, b>-5

400

l10p-4l - 1 < 33

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<1, x>-5

400

2lx+9l + 3 > 7

x>-7,x<-11

500

3lx/7l>21

x>49,x<-49