Solving "Simple" Inequalities
Compound Inequalities
Absolute Value Equations
Absolute Value Inequalities
Writing Inequalities & Other Stuff
100
Solve: x + 8 < -3
x < -11
100
Graph: -2 < x <= 3
See board
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| < 4

-15 < 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
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: |-5x + 8| > 12

x<-4/5 or x>4

500
Will needs at least 800 points to be a finalist on a game show. He currently has 640 points with one round to go. Which inequality could be solved to determine the number of points needed in the last round in order for him to be a finalist? A) 640 + x <= 800 B) 640 + x >= 800 C) x - 800 >= 640 D) 640 + 800 > x
B
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