Absolute Value Equations and Inequalities

"One-Step" Absolute Value Equations

100

l3xl=27

What is x=-9,9

200

lx+5l=10

What is x=-15, 5

300

l4x+22l=30

What is x=-13, 2

400

l17d/4l=127

x=-508/17,508/17

500

|(4-7x)/3|=4

What is x = -8/7 or x = 16/7

Multi-Step Absolute Value Equations

100

lv+8l-5=2

What is v=-15,-1

200

l5xl+5=45

What is x=-8,8

300

6l1-5xl-9=57

What is x=-2, 12/5

400

l8x+4l/2=16

What is x=-9/2,7/2

500

2l28x+4l+6=12

What is x = -1/4 or x = -1/28

Compound Inequalities

100

x + 5 > 10 or 2x<20

What is x > 5 or x < 10

200

-19 < 2x - 3 < 11

What is -8 < x < 7

300

-38 < -5x + 7 < -13

What is 4 < x < 9

400

[3(x - 7)]/2 < 3 or 8(x - 7) > 32

What is x < 9 or x > 11

500

-17n - 12 < 13n - 12 < -8 + 9n

What is 0 < n < 1

"One-Step" Absolute Value Inequalities

100

l6nl<18

What is -3 < n < 3

200

lx-2l<8

What is -6 < x < 10

300

l1-6bl>4

What is b<-1/2 or b>5/6

400

|(2-3x)/2| > 5

What is x < -8/3 or x > 4

500

|[3(2-x)]/5| < 20

What is -94/3 < x < 106/3

Multi-Step Absolute Value Inequalities

100

lx+2l+2<4

What is -4 < x < 0

200

2lx+3l+4>8

What is x < -5 or x > -1

300

-2lx+2l-1<-8

What is -11/2<x<3/2

400

3-2l4x+9l>-11

What is -4 < x < -1/2

500

-|9-3x| + 3 > 0

What is 2 < x < 4