Absolute Value Functions Review

Absolute Value Functions Review

Let's summerize our learning.

Multiple Choice

True or False

The absolute value of a number can be positive or negative?

• True

• False

• I really don't know

Multiple Select

The |x| can be . . .

• A numbers less than 1

• Zero

• Negative Numbers

• All real numbers

• non-negative numbers

The Algebraic Definition of Absolute Value

What does that mean?

Multiple Select

 $\left|x\right|\ =\ 5\ ,\ meaning\ the\ value\ of\ x\ is\$  

• 5

• -5

• No solution

• All real numbers

Absolute Inequalities

Inequality is a universal topic in math. The rules are the same as they were linear equations.

Multiple Choice

 $\left|z\right|>8$  

Solve the inequality

•  $z=-8\ or\ z\ =\ 8$  

•  $z\ <8$  

•  $-8<z<8$  

•  $z<\ -8\ \ \ or\ \ \ \ \ z\ >8$  

Absolute Value Equations & Inequalities

Not all equations or Inequalities require solving.

Multiple Choice

 $Solve$   $\left|x\right|\ =\ -5$  

•  $x\ =\ -5$  

•  $x\ =\ 5$  

•  $x\ =\ 5\ or\ -5$  

• No Solution

Multiple Choice

 $Solve:\ \ \left|x-3\right|\ +7\ =\ 2$  

• All real numbers

• x = -2

• x = -2 & 8

• No Solution

 $Solve:\ \ \ \ \left|x-3\right|+7=2$  

• First step is to subtract 7 on both sides. We want to isolate the absolute value

• The equation then becomes  $\left|x-3\right|=-5$  

• Absolute value cannot be negative. 

• There are NO SOLUTIONS

Multiple Choice

 $Solve:\ \ \ \ \ \ -7<\left|3x+1\right|\$  

• No Solution

• x = 2
  

• x = -2  or x = 2

• All Real Numbers

 $-7<\left|3x+1\right|$  

This is equivalent to 
 $\left|3x+1\right|>-7$  
Absolute Value is ALWAYS 

greater than a negative

Poll

Who needs support with solving absolute value equations?

• I'm good

• I need help

• I don't even know