Absolute Value and Inequalities Review

Absolute Value and Inequalities Review

Multiple Choice

| –3 |

• 3

• -3

• 0.30

• 30

Let's Review Absolute Value 

Absolute Value makes values positive; it means the distance from zero 

Open Ended

_{What does Absolute Value do?}

Multiple Choice

| –3 |

• 3

• -3

• 0.30

• 30

Solving Absoulte Value Equations 

When we solve absolute value equations we set the Absolute Value expression to the negative and positive answer. Most of the time you will have 2 different solutions.

Multiple Choice

Solve for a: |2a + 10| = 6

• a = 8, a = 2

• a = -8

• a = −2

• a = −8, a = −2

Multiple Choice

Solve for x: ∣ 2x + 9 ∣ = 15

• x = 3

• x = 3, x = −12

• x = 3, x = −6

• x = 6, x = −12

Multiple Choice

|v + 8| − 5 = 2

• v= -15 , v= 15}

• v = -1 v = -5}

• no solution

• v = -1 , v= -15

Solving Simple Inequaltities 

You solve inequalites just like and equations accept they have <, ≤, > or  ≥  signs. Remember; When you divide by a negative you have to flip the sign!

Multiple Choice

Solve the inequality.

x + 5 ≤ 13

• x ≥ 8

• x ≥ 18

• x ≤ 8

• x ≤ 18

Multiple Choice

Which is the solution of

-4 - 6m > -9m + 8?

• m < -4

• m > 4

• m < 15

• m > 36

Multiple Choice

• 11 < a

• 11 ≤ a

• 11 > a

• 11 ≥ a

Compound Inequalities 

Compound inequalities are made up of two simple inequalities. When we solve compound inequalities we need to solve two seperate simple inequalies. 

Multiple Choice

Solve and graph:

• A

• B

• C

• D

Multiple Choice

Solve: 0 < x + 7 < 9

• -7 < x and x < 2

• -7 < x or x < 2

• -7 > x and x > 2

• -7 > x or x > 2

Multiple Choice

What is inequality is graphed?

• x > 2 and x ≤ -3

• x > 2 or x ≤ -3

• x > 2 and x < -3

• x > 2 or x < -3

Interval Notation

Interval notations is another way to write an inequalities. It is very useful when describing the graph of inequalities. 

Multiple Choice

Express the following in Interval Notation

-8 ≤ x < 8

• [-8, 8]

• (-8, 8]

• [-8,8)

• (-8, 8)

Multiple Choice

Write the following in interval notation

x < 8

• (8, ∞)

• (-∞, 8)

• (8, -∞)

• [-∞, 8]

Multiple Choice

Express the following interval in Set notation:

[3, 5]

• 3 ≤ x ≤ 5

• 3 ≤ x < 5

• 3 < x ≤ 5

• 3 < x < 5