1. Solving Open Sentences Involving Absolute Value
Lesson 6-5
Solving Open Sentences Involving Absolute Value

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4. Objectives Solve absolute value equations
Solve absolute value inequalities

5. Vocabulary
none

6. 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

7. 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

8. 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

9. 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 .

10. Example 2 cont
Answer:
Check Substitute –4 and 6 into

11. Example 3 Then graph the solution set. Write as and Case 1 Case 2
Original inequality
Add 3 to each side.
Simplify.
Answer: The solution set is

12. Example 4 Then graph the solution set. Write as or Case 1 Case 2
Original inequality
Add 3 to each side.
Simplify.
Divide each side by 3.
Simplify.
Answer: The solution set is

13. Summary & Homework Summary: Homework: If |x| = n, then x = -n or x = n
If |x| < n, then x = -n or x = n (inside)
If |x| > n, then x = -n or x = n (outside)
Homework:
none n -n n -n n -n