Compound Absolute Values Equalities and Inequalities

1
Compound Absolute ValuesEqualities and
Inequalities

• More than one absolute value in the equation

2
Find a number that works.
Well, how can you find all of the solutions in a
more methodical way?
3
In your approach, think about the values of this
particular mathematical statement in the 3
different areas on this number line.
-2
1
4
What happens in the expression as x goes from
area 1, to area II, to area III?
I
II
III
-2
1
5
This is a domain limiting problem. How does
limiting the values that I am considering for x
help me evaluate the equation?

• Look at these 3 equations to see if you can
  figure out how we will limit the domain.

6
-2
2
-3
0
-5
7
Lets try a problem
8
We need a process

• Draw a number line to create areas of
• consideration (i.e. Limit the domain!!)
• Determine the value of each absolute value in
  each area (that is, is each absolute value
  positive or negative) and remove absolute values
  based on that.
• Solve the equation.
• 4. See where the domain overlaps with the answer
  for each area.

9
Why?

• If we pick a domain of possible answers, the
  solution of the equation gives the answers IN THE
  DOMAIN that actually work.
• So, the overlap (the intersection) of the two
  sets will be the answer for that particular
  limitation.

10
What does this mean?

• Each case will be an and within the case
  (domain w/answer)
• Take the 3 answers (case 1, case 2, case 3) and
  combine as an or.