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Solving "Simple" Inequalities
Compound Inequalities
Absolute Value Equations
Absolute Value Inequalities
Writing Inequalities & Other Stuff
100
Solve: x + 8 < -3
x < -11
100

Solve: -2 < x+1 < 3

-3 < x < 2

100
Solve: |x + 2| = 18
-20 and 16
100
If an absolute value expression is LESS than a number, is that an "AND" situation or an "OR" situation?
"AND" situation
100
Translate into an inequality: "4 more than a number is less than or equal to 16."
4 + x <= 16
200
Solve: 14 > 6x - 10
4 > x
200
Solve: 2x - 7 < 13 or x + 8 > 22
x < 10 or x > 14
200
Solve: |6x - 4| = -20
No solution
200
Solve: |x + 3| < 8
-11 < x < 5
200
When do you flip the sign of an inequality?
When you multiply or divide by a negative number
300
Solve: -7x + 3 < 45
x > -6
300

Solve: -15 < -3x + 6 < 3

7 > x >1

300
Solve: |3x - 12| = 9
7 and 1
300

Solve: |2x + 5| > 19

x > 7 or x < -12

300
Tracie has at least 57 gumballs in a jar. Write an inequality to represent the situation.
x >= 57
400
Solve: 9x + 5(3 - 2x) < -11
x > 26
400
Solve: -2x + 11 < 3 or x/3 - 1 < -10
x > 4 or x < -27
400
Solve: |2x - 6| + 8 = 20
9 and -3
400

Solve: |x + 11| - 7 > -3

x < -15 or x > -7

400

An electrician earns $35 an hour. He wants to earn at least $1500 a week. Which inequality could be solved to determine the number of hours he would need to work? 

A) 35h < 1500 

B) 35h > 1500 

C) 35h < 1500 

D) 35h > 1500

D) 35h > 1500

500
Solve: -3(6 - 2x) > 14 + 8x
-16 > x
500
Solve: -16 < 4(2x - 12) < 24
1 < x < 9
500
Solve: 2|x - 8| - 5 = 7
14 and 2
500
Solve: -5|x + 8| > 20
No solution
500

Will has at most $60 to spend on clothes. He wants to buy a pair of jeans for $22 and spend the rest on t-shirts. Each t-shirt cost $8. How many t-shirts can be bought? (Let x represent the number of t-shirts.)

A) 22 + 8x < 60

B) 22 + 8x > 60 

C) 22 - 8x < 60 

D) 22 - 8x > 60

A) 22 + 8x < 60