1. Solving Absolute Value Equations
LESSON 1–4
Solving Absolute Value Equations

2. A2.6(D) Formulate absolute value linear equations.
Targeted TEKS
A2.6(D) Formulate absolute value linear
equations.
A2.6(E) Solve absolute value linear equations.
Mathematical Processes
A2.1(B), A2.1(D)
TEKS

3. absolute value
empty set
constraint
extraneous solution
Vocabulary

4. Concept

5. Case 1 a = b y + 3 = 8 y + 3 – 3 = 8 – 3 y = 5 Case 2 a = –b
Solve an Absolute Value Equation
Case 1 a = b
y + 3 = 8
y + 3 – 3 = 8 – 3
y = 5
Case 2 a = –b
y + 3 = –8
y + 3 – 3 = –8 – 3
y = –11
Check |y + 3| = 8
|y + 3| = 8 ?
|5 + 3| = 8 ?
|–11 + 3| = 8 ?
|8| = 8 ?
|–8| = 8 
8 = 8 
8 = 8
Answer: The solutions are 5 and –11. Thus, the solution set is –11, 5.
Example 2

6. What is the solution to |2x + 5| = 15?
B. {–10, 5}
C. {–5, 10}
D. {–5}
Example 2

7. |6 – 4t| + 5 = 0 Original equation
No Solution
Solve |6 – 4t| + 5 = 0.
|6 – 4t| + 5 = 0 Original equation
|6 – 4t| = –5 Subtract 5 from each side.
This sentence is never true.
Answer: The solution set is .
Example 3

8. A. B. C. D.
Example 3

9. One Solution
Case 1 a = b
8 + y = 2y – 3
8 = y – 3
11 = y
Example 4

10. One Solution
Check: 
Answer:
Example 4

11. A. B. C. D.
Example 4

12. Solving Absolute Value Equations
LESSON 1–4
Solving Absolute Value Equations