Absolute Value Equations and Inequalities

One-Step Absolute Value Equations

100

Solve l3xl=27

x=-9,9

200

What is lx+5l=10?

x=-15, 5

300

Solve l4x+22l=30

x=-13, 8

400

Solve l8p/3l=4

p=-3/2,3/2

500

Solve l17d/4l=127

x=-508/17,508/17

Multi-Step Absolute Value Equations

100

Solve lv+8l-5=2

v=-15,-1

200

Solve l5xl+5=45

x=-8,8

300

Solve 6l1-5xl-9=57

x=-2, 12/5

400

Solve l8x+4l/2=16

x=-9/2,7/2

500

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

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

Extraneous Solutions

100

Does lx+3l=4 have an extraneous solution?

If so, what is it/them?

No extraneous solution

200

Does l2xl=-4 have an extraneous solution?

If so, state it/them.

No solutions: x=-2, x=2 are both extraneous

300

Can all solutions be extraneous?

yes

400

What is the extraneous solution of l3x+2l=4x+5?

x=-3 is extraneous and x=-1 is a solution

500

What is the extraneous solution for l2x+5l=3x+4?

x=1 is a solution, x=-1.8 is extraneous

One-Step Absolute Value Inequalities

100

Solve l6nl<18

n<3,n>-3

200

Solve lx-2l<8

x<10,x>-6

300

Solve l1+bl<4

b<3, b>-5

400

Solve l10p-4l<34

p<19/5, p>-3

500

Solve l5+b/5l<10

b<25, b>-75

Multi-Step Absolute Value Inequalities

100

Solve lx+2l+2<4

x>-4 and x<0

200

Solve 2lx+3l>8

x<-7 or x>1

300

Solve 2lx+2l-1<8

x<1 and x>-5

400

Solve 2lx+9l+3>7

x>-7 or x<-11

500

Solve 3lx/7l+2>23

x>49 or x<-49