Chapter 2 Review

Solving Absolute Value Equations

100

|x+5|=12

x = 7 and x = -17

200

|2x+7|+3=14

x = 2 and x = -9

300

-2|3x-1|=10

No Solution

400

3|x+2|-5=16

x = 5 and x = -9

500

(1/2)|5-4x|+2=10

x = -11/4 and x = 21/4

Checking for Extraneous Solutions

100

|2x-3|=x+6

x = 3 and x = -3

9 = 9 and 3 = 3

Both x = 3 and x = -3 are solutions

200

|x-5|=3x+1

x = 1 and x = -3

4 = 4 and 8 = -8

x = 1 is a solution

x = -3 is EXS

300

|x+7|=4x+1

x = 2 and x = -1.6

9 = 9 and 8.6 = 7.4

x = 2 is a solution

x = -1.6 is EXS

400

|2x-8|+3=-x+4

x = 9 and x = 3

13 = -5 and 5 = 1

Both are EXS

500

(1/2)|x+4|-3=2

x = -2 x = -14/3

-2 = 2 and -2/3 = 2

Both are EXS

Solving Multi-Step Inequalities

100

2x+5 > 13

x > 4

200

4(x-2) < 16

x < 6

300

3(2x-4) < 4x+6

x < 9

400

6 - 2(x+5) > 4x - 16

x < 2

500

2(3x-5) - 4x > 2(x-6)

All Real Numbers

Solving Compound Inequalities

100

-3 < x + 2 < 7

-5 < x < 5

200

2x - 1 < -5 or 3x + 2 > 11

x < -2 or x > 3

300

3 < 2x - 1 < 9

2 < x < 5

400

3x + 1 < -8 or -2x + 3 < -5

x < -3 or x > 4

500

-4 < (2x+2)/3 < 4

-7 < x < 5

Solving Absolute Value Inequalities

100

|2x - 1| > 9

x > 5 or x < -4

200

|4x - 2| + 3 < 11

x < 5/2 and x >-3/2

300

-2|x + 1| < -8

x > 3 or x < -5

400

|5x - 10| + 3 <=3

"|5x - 10| + 3 is less than or equal to 3"

x is less than or equal to 2 AND

x is greater than or equal to 2 THEREFORE

x = 2

500

(|4x - 1|/3) + 3 > 6

x > 5 or x < 1/2