6-5A Solving Absolute Value Equations

1
6-5A Solving Absolute Value Equations
Get branching technique from Teresa regarding
absolute value problems!
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
2
Absolute value is the distance a number is from
zero. Distance is never negative!
3
An absolute value equation is an equation of the
form
The value of c cannot be less than zero because
absolute value always indicates a number that is
NOT negative. To solve absolute value equations,
write the two related linear equations and then
solve them.
There are two values of x that have an absolute
value of 8.


8
-8
These are the two related linear equations!
The equations are solved because the variable is
isolated!
4
How to Solve Absolute Value Equations.
1. Write the absolute value equation.
2. Isolate the absolute value on one side of the
equal sign.
3. Write the two related linear equations.
Note These equations will NOT have absolute
value bars!
4. Solve each equation independently.
no solution
An absolute value equation can have two
solutions, one solution or no solution.
5
Solve. Then graph the solution.
Example 1
Example 2
Example 3
Example 4
6
Example 1 Solve. Then graph the solution.
24, -24


24
-24
Example 2 Solve. Then graph the solution.
no solution
?
7
Solve. Then graph the solution.
Example 4
Example 3
or
or
-4, 12




-4
12
5
8
Solve.
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
9
Solve.
Example 6
Example 5
No solution
The absolute value of a number is never negative!
or
You can NOT distribute through absolute value
bars!
-4, 1
Note Before you can write the two related
linear equations you must isolate the absolute
value!
10
Solve.
Example 8
Example 7
or
or
3, 4
-6, -4
11
Solve.
Example 10
Example 9
No solution
The absolute value of a number is never negative!
or
-2, 10
12
Example 10
Check by substitution.
13
Homework
6-A10 Pages 325327 718 (do not graph), 5358.