

Absolute Value Intro
Presentation
•
Mathematics
•
9th - 12th Grade
•
Hard
Joseph Anderson
FREE Resource
10 Slides • 13 Questions
1
Introduction to Solving Absolute Value Equations
Let's start at the beginning!

2
Multiple Choice
The absolute value of a number represents the ___________ from that number to zero on a number line.
distance
journey
transformation
dissolution
3
Multiple Choice
Evaluate: |-6|
6
-6
1
0
4
Multiple Choice
Evaluate: |6|
6
-6
0
1
5
Absolute Value
The distance from zero on a number line.
| -6 | = 6 means that the value -6 is six steps away from zero on a number line.
So what if we know the distance? How can we figure out what the value is?
6
Multiple Select
Which of the following could I substitute in for x and get 3?
∣x∣=33
-3
0
1
7
There are 2 answers!
"What are two numbers that are 3 units away from 0?"
Two values work!
x = -3 or x = 3
8
Multiple Select
What about this one? Which of the following values could I substitute in for x and it would make a true sentence?
∣x−2∣=33
-3
-1
5
2
9
Use Substitution
Let x = -1
| -1 - 2 | = | -3 | = 3
Let x = 5
| 5 - 2 | = | 3 | = 3
10
What about this one?
|2x+7| = 5
If we weren't given multiple choice answers, we could guess until we found values that worked.
However, there are steps to solve.
11
Steps for Solving Absolute Value Equations
ISOLATE the Absolute Value BARS
SPLIT into two equations: the positive case and the negative case
SOLVE each equation
CHECK each solution using substitution into the original equation
12
Multiple Choice
What does it mean to "isolate the bars?"
How would you isolate the bars for this equation:
Add 3 to both sides
Subtract 3 from both sides
Add 10 to both sides
Subtract 10 from both sides
13
We isolate the bars just as we would isolate a variable in a regular equation.
∣x∣−3=10
∣x∣−3+3 = 10+3 (Adding 3 to both sides)
∣x∣=13
For this problem, we see a couple of solutions for x.
-13 and 13
14
Multiple Choice
How about this one? How would you isolate the bars?
4∣x∣=16Add 4 to both sides
Subtract 4 from both sides
Multiply 4 on both sides
Divide both sides by 4
15
Multiple Choice
How about this one?
Isolate the bars:
Add 4 to both sides
Subtract 4 from both sides
Multiply 4 on both sides
Divide both sides by 4
16
Multiple Choice
How about this one?
Isolate the bars:
Add 2 to both sides
Subtract 2 from both sides
Multiply 4 on both sides
Divide both sides by 4
17
Whatever is inside the bars...
...stays inside the bars when you are isolating. Don't mess with the inside!
18
Multiple Choice
Isolate the bars......
∣x+3∣=6
∣x∣=3
∣x+5∣=8
∣5x∣=8
19
Multiple Choice
Isolate the bars......
∣x−8∣=4
∣x∣=12
∣5x−40∣=20
∣5x−47∣=13
20
So we know how to isolate the bars...then what?
Split into two equations
21
Split into two equations:
The positive case: x+3=6 which can be solved --> x = 3
The negative case: x+3=−6 which can be solved --> x = -9
22
Multiple Select
Split into two equations:
∣2x+7∣=52x+7=5
−2x+7=5
2x+7=−5
−2x−7=−5
23
Multiple Select
Isolate the bars and Split into two equations:
∣x−8∣+2=5x−8=3
x−8+2=5
x−8=−3
x−8+2=−5
Introduction to Solving Absolute Value Equations
Let's start at the beginning!

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