Download Lesson 6-5 Solving Open Sentences Involving Absolute Value

Lesson 6-5
Solving Open Sentences
Involving Absolute Value
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Objectives
• Solve absolute value equations
• Solve absolute value inequalities
Vocabulary
• none
Steps for Solving Equations
• Step 1: Use the Distributive Property to remove the
grouping symbols, () or []
• Step 2: Simplify the expressions on each side of the
equal sign “=” by combining like terms (variable and
#’s)
• Step 3: Use the Addition and /or Subtraction
Properties of Equality to get the variables on one
side of the equal sign and the numbers without
variables on the other side of the equals sign
• Step 4: Simplify the expressions on each side of the
equals sign by combining like terms
• Step 5: Use the Multiplication and/or Division
Properties of Equalities to solve for the variable
Example 1
Method 1 Graphing
means that the distance between b and –6
is 5 units. To find b on the number line, start at –6 and
move 5 units in either direction.
The distance from –6 to –11 is 5 units.
The distance from –6 to –1 is 5 units.
Answer: The solution set is
Example 1 cont
Method 2 Compound Sentence
Write
as
or
Case 1
Case 2
Original inequality
Subtract 6 from
each side.
Simplify.
Answer: The solution set is
Example 2
Write an equation involving the absolute value for
the graph.
Find the point that is the same distance from –4 as the
distance from 6. The midpoint between –4 and 6 is 1.
The distance from 1 to –4 is 5 units.
The distance from 1 to 6 is 5 units.
So, an equation is
.
Example 2 cont
Answer:
Check Substitute –4 and 6 into
Example 3
Then graph the solution set.
Write
as
and
Case 2
Case 1
Original inequality
Add 3 to each side.
Simplify.
Answer: The solution set is
Example 4
Then graph the solution set.
Write
as
or
Case 2
Case 1
Original inequality
Add 3 to each side.
Simplify.
Divide each side by 3.
Simplify.
Answer: The solution set is
Summary & Homework
• Summary:
– If |x| = n, then x = -n or x = n
-n
0
n
– If |x| < n, then x = -n or x = n (inside)
-n
0
n
– If |x| > n, then x = -n or x = n (outside)
-n
• Homework:
– none
0
n