Compound Inequalities and Absolute Value

Vocab/Translate

100

Closed or open circle? >

open

200

Write the inequality for "less than or equal to"

 ≤

300

Translate: a number is greater than 5

x > 5

400

the product of a number and 3 is less than 18

3x < 18

500

What is the word for two or more inequalities that use "and" or 'or' ?

Compound Inequalities

Inequalities

100

Give the graph for:

x > 7

open circle going right

200

Graph and give the interval notation:

x  ≤  -8

closed circle at -8 going to the left

(-∞, -8]

300

Solve the inequality:

2x + 5 ≥ 11

 x ≥ 3

400

Solve the inequality and graph and give interval notation:

3x - 11 < 10 

x < 7

Graph is open circle at 7 going left

(-∞, 7)

500

Solve the inequality and graph and give interval notation:

-2x -18  ≤ -26

x ≥ 4

Graph: closed circle at 4 going right

[4, ∞) 

Compound Inequalities

100

Graph and give interval notation:

-3 < x < 4

Graph: open circles at -3 and 4 and they are connected

(-3, 4)

200

Graph and give interval notation:

x < -4  or  x ≥ 0

Graph: Open circle at -4 going left and a closed circle at 0 going right

(-∞, -4) or [0, ∞)

300

Solve and graph and give interval notation:

 3x < - 9  or  x - 3 ≥ 1 

x < -3 or x ≥ 4

Graph: open circle at -3 going left and closed circle at 4 going right

(-∞, -3) or [4, ∞)

400

Solve and graph and give interval notation:

- 1 ≤ x + 3 < 2 

-4  ≤ x  < -1

Graph: closed circle at -4 and open circle at -1 and connected [-4, -1)

500

Solve and graph and give interval notation:

-2 < -2/3 x + 4 < 6 

9 > x > -3     or    -3 < x < 9

Graph: open circles at -3 and 9 and connected

(-3, 9) 

Absolute Value Equations

100

solve: 

|x| = 5

{-5, 5}

200

Solve: 

|x| = -2

No solution

300

Solve:

|2x| = 8 

{-4, 4}

400

Solve:

| 4x - 8 | = 32

{-6,10}

500

Solve:

-2|x+ 5| + 8 = 6 

{-6, -4}

Absolute Value Inequalites

100

Will this be an "and" or an "or"?

<

AND

200

Solve:

|x| > 9

x > 9 or x < -9

300

Solve and graph and give interval notation:

|x| < 5

-5 < x < 5 

Graph: open circles and -5 and 5 and connected

(-5, 5)

400

Solve and graph and give interval notation:

|x+3| ≤ 2

-5 ≤ x ≤ -1

Graph: closed circles at -5 and -1 and connected

[-5, -1] 

500

Solve and graph and give interval notation:

|2x - 1| - 9  > 8

x > 9 or x < -8

Graph: open circle at -8 going left and open circle and 9 going right

(-∞, -8) or (9, ∞)