Solving Inequalities and Absolute Value Equations/Inequalities

Solving Equations

100

Solve: n - 5 = n - 3

No Solution

200

Solve : 4x + 9 = 2x - 6

x = -15/2 or x = - 7 1/2

300

Solve: 4(x+6) - 11 = 25

x=3

400

Solve: 2(x-5) = 5(x+5) -2 

x = -11

500

Solve the equation: 

2(4x-6) = -10 +8x - 2

All Real Numbers/ Infinite solutions

Multi-Step Inequalities

100

9x – 6 < 3

What is x<1

200

20+4x>2(x+20)

What is x>10

300

4(-x+3)>-4x+6

What is all real numbers

400

10x-10-7x>3x-2

What is no solution

500

17-(4x-2)<2(x+3)

What is x>13/6

Compound Inequalities

100

Write a compound inequality for all real numbers that are greater than –8 and less than 8

-8<x<8

200

Solve -2<-2x-4<8

What is -1>x>-6

-6<x<-1

300

Solve -2<4x-10<6

2<x<4

400

Solve 

2x – 2 < –12 OR 2x + 3 > 7

x <-5 OR x > 2

500

Solve 12h-3>=15h or 5>-0.2h+10

h < -1 OR h>25

Absolute Value

100

Solve |x|+10=1

no solution

200

Solve 6|n|-2=10

What is n=2 or n=-2

300

Solve |9x|=27

What is x=-3,3

400

2 +|9-k|=13

What is k= -2,20

500

10|4x-2|-7=93

x = -2, 3

Isolate the variable /Word Problems/ absolute value

100

Solve for P  in A = 2B + Ph

P = (A-2B)/ h

200

Solve for y: 2x + 3y = 7

y = (7-2x)/3 or y = 7/3 -2/3x

300

John wants to save at least $750 for an upcoming vacation.  He has $300 already saved and saves an additional $25 each week.  Figure out the number of weeks it will take John to save enough for his vacation.

300 + 25x >= 750

25x >= 450

x >=18

He needs to save for at least 18 weeks

400

-|6x| < -30

x > 5 or x< -5

500

10-|7- 10x| < -77

x< -8 or x> 47/5