1. Solving Absolute Value Equations

2. Vocabulary Solving Absolute Value Equations
Evaluate expressions involving absolute values.
Solve absolute value equations.
Vocabulary
1) absolute value
2) empty set

3. Solving Absolute Value Equations
Seismologists use the Richter scale to express the
Magnitudes of earthquakes. This scale ranges from 1 to
10, 10 being the highest.
The uncertainty in the estimate of a magnitude E is about
Plus or minus 0.3 unit.
This means that an earthquake with a magnitude estimated
at 6.1 might actually have a magnitude as low as 5.8 or as
high as 6.4.
These extremes can be described by the absolute value equation
Richter Scale 10 E

4. Solving Absolute Value Equations
The absolute value of a number is its distance from zero on the number line.
Since distance is nonnegative (positive), the absolute value of a number is always
nonnegative.

5. Solving Absolute Value Equations
The absolute value of a number is its distance from zero on the number line.
Since distance is nonnegative (positive), the absolute value of a number is always
nonnegative.
is used to represent the absolute value of a number x.
The symbol

6. Solving Absolute Value Equations
For any real number a,
if a is positive or zero,
the absolute value of a is a.
For any real number a,
if a is negative,
the absolute value of a is a.
distance from
zero = a
distance from
zero = a -a a
For any real number a,
and

7. Solving Absolute Value Equations

8. Solving Absolute Value Equations
negative side:
positive side:

9. Solving Absolute Value Equations
negative side:
positive side:
Solution set is: { 8, 42 }

10. Solving Absolute Value Equations
Step 1) Isolate the absolute value expression by dividing both sides of the
equation by 3.

11. Solving Absolute Value Equations
Step 1) Isolate the absolute value expression by dividing both sides of the
equation by 3.

12. Solving Absolute Value Equations
Step 1) Isolate the absolute value expression by dividing both sides of the
equation by 3.
negative side:

13. Solving Absolute Value Equations
Step 1) Isolate the absolute value expression by dividing both sides of the
equation by 3.
negative side:
positive side:

14. Solving Absolute Value Equations
Step 1) Isolate the absolute value expression by dividing both sides of the
equation by 3.
negative side:
positive side:

15. Solving Absolute Value Equations
Step 1) Isolate the absolute value expression by dividing both sides of the
equation by 3.
negative side:
positive side:

16. Solving Absolute Value Equations
Step 1) Isolate the absolute value expression by dividing both sides of the
equation by 3.
negative side:
positive side:

17. Solving Absolute Value Equations
Step 1) Isolate the absolute value expression by dividing both sides of the
equation by 3.
negative side:
positive side:

18. Solving Absolute Value Equations
Step 1) Isolate the absolute value expression by dividing both sides of the
equation by 3.
negative side:
positive side:

19. Solving Absolute Value Equations
Step 1) Isolate the absolute value expression by dividing both sides of the
equation by – 12.
Absolute values are all NONNEGATIVE!

20. Solving Absolute Value Equations
Step 1) Isolate the absolute value expression by dividing both sides of the
equation by – 12.
Absolute values are all NONNEGATIVE!
This is referred to as an EMPTY SET.