NC.M3.U1.A-CED.1&2 Re-Test Lesson

​NC Math 3 Unit 1 Re-Test Lesson
Standard(s): A-CED.1&2

​Instructions:
Earn an 80% or higher on this lesson to be able to re-attempt the questions that you missed tied to this standard from our Unit 1 test.

Absolute Value is the distance from zero.

**ALWAYS POSITIVE**

• Distance is NEVER negative
  (for example: when you travel, you always travel in positive miles... you NEVER say " I went negative 5 miles back home.)

Multiple Choice

What is the reason that absolute value is always written as a positive?

• Absolute value is talking about numbers so it must be positive.
• Absolute value does not always have to be positive.
• Absolute value is like a clock it has only positive numbers.
• Absolute value is talking about distance, distance is always measured by positive numbers.

Multiple Choice

What is the absolute value of |-26|.

• 26

• -26

• 0

• -20

Multiple Choice

What is the absolute value of |6|.

• 6

• -6

• 0

• undefined

​How to solve Absolute Value Equations

1. ​Isolate the Absolute Value

2. ​Create 2 Equations

   1. ​Equation #1: Set "inside" equal to the positive of the other side.

   2. ​Equation #2: Set "inside" equation to the negative of the other side.

3. ​Solve each equation

4. ​Write answer as a solution set

​The solutions are x = 10.5 and x = -5.5

Multiple Choice

∣ 2x + 9 ∣ = 15

• {3}

• { -6,3}

• { -12,3}

• { -12,6}

​Lesson: Isolating the Absolute Value

​Complete your notes using the video below.

​The solutions are x = 1 and x = -15.

Multiple Choice

−2|−2r − 4| = -12

• {5,1}

• {-5,1}

• {-5}

• No Solution

Multiple Choice

 |−2n| + 10 = −50

• {30, -30}
• {20,-20}
• {-5,5}
• No Solution

Solve absolute value inequalities

Multiple Choice

Solve the absolute value inequality:

$$\left|2x-5\right|<23$$  

• $$9<x\le-14$$  
  

• $$-14<x<-9$$  
  

• $$-9\le x\le14$$  
  

Multiple Choice

Solve the absolute value inequality:

$$\left|x+7\right|>10$$  

• -17 < x < 3

• x < -17  or  x > 3

• x > 3

• x < -17

Multiple Choice

Solve the absolute value inequality:

$$\left|x+2\right|\ge3$$  

• $$x\le-5\ \ or\ \ \ x\ge1$$  
  

• $$x\le-5$$  
  

• $$x>1$$  
  

• $$-5<x<1$$  
  

Multiple Choice

Solve the absolute value inequality:

$$\left|x-7\right|<6$$  

• $$-10<x<-4$$  
  

• $$-12<x<-2$$  
  

• $$1\le x\le13$$  
  

• $$1<x<13$$  
  

Multiple Choice

Solve the absolute value inequality:

$$\left|2x-5\right|<23$$  

• $$9<x\le-14$$  
  

• $$-14<x<-9$$  
  

• $$-9\le x\le14$$  
  

Absolute Value Word Problems

Multiple Choice

What's a way to define absolute value?

• The value of a number
• The opposite of a number
• The distance of a number from zero
• The multiplicative inverse of a number

Multiple Choice

A company sells 20-ounce bottles of sports drink. The actual volume of liquid in the bottle must be within 0.03 ounces. What equation can be solved to find the minimum and maximum volume of liquid in a bottle.

• |v|-20=0.03
• |v-20|=0.03
• |v|-0.03=20
• |v-0.03|=20

Multiple Choice

Your have money in your wallet, but you don't know the exact amount. When a friend asks you, you say that you have 50 dollars give or take 15. Write an absolute value equation to model this situation.

• |x-50|=15
• |x+15|=50
• |50+x|=15
• No Solution

Multiple Choice

Write an absolute value function given the following transformations:

Horizontal shift left 1 unit

Vertical shift down 9 units

• f(x) = |x + 1| - 9

• f(x) = |x - 1| - 9

• f(x) = |x - 1| +9

• f(x) = |x + 9| - 1

Multiple Choice

Describe the transformation of the equation below from the parent function of

y = IxI ,

y = I x + 2 I - 5

• Left 2 up 5

• Right 2 up 5

• Left 2 down 5

• Right 2 down 5

Multiple Choice

$$y=-\frac{1}{2}\left|x\right|+2$$  Which of the following graphs matches the equation

Multiple Choice

Which of the following equations matches the graph?

• $$y=\left|x-3\right|+2$$

• $$y=-\left|x-3\right|+2$$

• $$y=\left|x+3\right|+2$$

• $$y=\left|x+3\right|-2$$