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=-508/17,508/17

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

2| 4x-5 | +7 = 3

no solution

Basic absolute value inequalities

100

| 6n |<18

-3<n<3

200

| x-2 | >8

x< -6 or x>10

300

| 1+2x| <7

-4<x<3

400

| 10p-4 |<34

-3<p<19/5

500

| 3x+2 | > 8

x < -10/3 or x > 2

extra step Absolute Value Inequalities

100

-5|9r+1|<-40

r<-1 or r>7/9

200

10| -3p-5|>70

p<-4 or p>2/3

300

|-4+6x|-5<32

-5<x<22/3

400

4|-6+5n|<56

-8/5<n<4

500

-9|x-1|>-18

-1<x<3

Multi-Step Absolute Value Inequalities

100

10|6-5n|+7<117

-1<n<17/5

200

4|-2b-9|>70

b<-37 or b>57/2

300

-10|-3b+4|+3<-67

b<-1 or b>11/3

400

5|-4x+6|-5<25

0<x<3

500

9+2|2a+5|<-33

no solution