Unit 1: Equations & Inequalities Review

Absolute Value Equations

100

|x| = 4

{-4,4}

200

|x+4| = 16

{-20,12} 

300

|-4+5x| = 16

{4,-12/5}

400

3|-8x| + 8 = 80

{-3,3}

500

5|9-5n| - 7 = 38

{0, 18/5}

Inequalities

100

2x + 4 > 24

x>10

200

-b - 2 > 8

b<-10

300

-90 > -5(k-3)

k>21

400

-2(2-2x) - 4(x+5) </= -24

{All real Solutions}

500

3(1-2x)>3-6x

No Solutions

Compound Inequalities

100

2 < 2x < 6

1<x<3

200

6< x+6<11

0<x<5

300

9+2b<7 or 7-5b<-8

b<-1 or b>3

400

12+ 4n > 44 or 10 - 12n >  -38

n>8 or n<4

500

5v+10 < -4v-17 < 9-2v

-13<v<-3

Abs. Value Inequalities

100

|x/6| > 5

x>30 or x< -30

200

|-8n|<32

-4<n<4

300

|7x+4| > 74

x>10 or x<-78/7

400

(|x-4|)/5<2

-6<x<14

500

9|1+8n|-3>78

n>1 or n<-5/4

Miscellaneous

100

When is a closed dot used when graphing?

When graphing a less than or equal to sign or a greater than or equal to sign

200

When is an open dot used when graphing?

 When graphing a less than or a greater than sign

300

Define an extraneous solution

Solution that does not work in the original equation

400

Solve: |x| = -10

NO SOLUTIONS!

500

Name a number in each of the following sets (no repeat numbers):

Irrational, Rational, integer, whole number, natural number