Name_______________________________________ Date Watched___________________
Unit 4 – 1 Variable Equations – Lesson 7 – Solving Equations with Absolute Values
Essential Question:
1. What is absolute value?
2. What types of solutions can absolute value equations have (3 types)?
3. How do I solve equations that contain absolute value expressions?
Absolute value review:

Absolute value is _______________________________________________________________.

Examples:
|5| = ________________

|-5| = ________________
So, what is always true about the answer to an absolute value?
o Since absolute value measures ______________________, absolute value is always
equal to a ________________________________________.
o Each positive absolute value has _______ _____________________ that are that distance
away.
What can x be?
|x| = 5
RULE: _____________________________________________________________________________
What can q be?
REMEMBER: ** Almost Every ** absolute value equation was _______ solutions.
|q| = 100
An absolute value equation has 2 solutions when the absolute value is equal to a
_________________________ __________________.
Special Solutions:
*SOME* absolute value equations have ___________ solution and *SOME* absolute value equations
have ___________ solution.
|x| = -2
|x| = 0
Types of Solutions to Absolute Value Equations:
When the absolute value symbols are ______________________________, if…
1. the absolute value equals a _________________________, there will be __________________
2. the absolute value equals _________________________, there will be ____________________
3. the absolute value equals a _________________________, there will be __________________
Steps to Solving Absolute Value Equations:
1. _______________________ the absolute value symbols.
2. Observe whether your absolute value equation will have ________, ________, or _________
solution.
3. If _____________ solutions
exist, understand that the value
inside of the absolute value
symbols could be positive or
negative (±), create two
equations that can be used to
find the two solutions, and
solve.
3. If _____________ solution
exists, set the value inside of the
absolute value equal to zero and
solve.
3. If _____________ solution
exists because the absolute
value equals a negative amount,
write no solution.
2 Solution Examples:
x 3  4
x  12  40
4 x  2  20
2x  2  8
1 Solution Examples:
x 1  0
x3 4  4
8  x  2 8
No Solution Examples:
5  x  2 8
2  2x  5  7
Real World Situation:
A quality control inspector at a bolt factory examines random bolts that come off the assembly line. Any
bolt whose diameter differs by more than 0.04mm from 6.5mm is sent back. Let d equal the diameter of
a bolt. Solve the equation |d – 6.5|=0.04 to find the maximum and minimum diameters of an acceptable
bolt.
Let’s Review:
There are ______________________ different types of solutions to absolute value equations.
When the absolute value symbols are __________________, if….
1. The absolute value equals a ___________________ number, there will be ___________ solutions.
2. The absolute value equals ___________________ number, there will be ___________ solution.
3. The absolute value equals a ___________________ number, there will be ___________ solution.
Steps to Solving Absolute Value Equations:
*** SEE CHART ABOVE ON PAGE 2 ***
Reflection Questions:
1. Can you define absolute value?
yes
or
2. Can you isolate the absolute value symbols by using inverse operations?
yes
or
no
no
3. When the absolute value symbols are isolated, can you decide whether the equations will have 2,
1, or no solution?
yes
or
no
4. Can you solve an absolute value equation?
yes
or
no
5. Do you want to meet with Mrs. Daniel during study hall about this lesson? yes
or
no
Practice Problems: Solve each equation.
 6  x  4  6
2|x+2| = 48
3 x  4  0