AFDA – Unit 3: Absolute Value + Piecewise Functions
Day 1 Notes: Absolute Value Equations
Name: _________________
Block: _____ Date:_______
Today you will learn how to…
 solve and graph one variable absolute value equations
 special cases of absolute value
A fire station is located on Main Street and has buildings at every block to the right and to the left.
Which building is 2 blocks away from the fire station? Explain your answer.
If we send someone to the building that is 2 blocks away from the fire station,
how will she know that she has arrived at the correct place?
How do we describe two numbers that represent the same distance from a
location?
Absolute Value is the distance between __________________________.
What does this mean in real life?
If |𝑥| = 4, what are the possible values of 𝑥?
Solve each of the following.
1. |𝑥| = 7
2. |𝑥| = 13
When solving absolute value equations, think about breaking the variable out of jail…
 Get rid of any guards with reverse PEMDAS.
 Once the guards are gone, rewrite as two separate equations.
 Solve each equation for each variable.
Solve each of the following:
1. |𝑥 − 3| = 8
3. |15 − 3𝑥| = 12
2. |𝑥 + 2| = 9
4. |3𝑥 + 4| = 20
1
5. − |5 − 3𝑥| = −2
2
7.
|3𝑣−2|
5
=4
9. −3|5𝑥 + 1| − 6 = −9
4
6. −5 | 𝑤 + 6| = −10
5
8.
|−2𝑔+8|
10.
4
=6
4|2𝑥 + 3| − 2 = 6
11.
13.
1
3
2
5
|2𝑥 − 5| + 3 = 7
7
|𝑥 − 5| − = 4
8
12.
14.
7
4
|3𝑥 + 5| + 1 = 15
1
−2 | 𝑠 − 5| + 3 = 8
3