1. 1.7: Solve Absolute Value Equations
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Absolute Value Equations
Section 1.7
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2. 1.7: Solve Absolute Value Equations
Definitions
Absolute Value is the distance from zero.
When graphing in Absolute Value, it is shaped in a “v”
>, <, or ≠ requires the dot being OPEN or PARENTHESIS
>, <, or = required the dot being CLOSED or BRACKETS
Extraneous Solutions are solutions that must be rejected because it does not satisfy the original equation
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1.7: Solve Absolute Value Equations

3. 1.7: Solve Absolute Value Equations
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Quick Examples
1) What is the absolute value of 25?
2) |–25| = x, what is/are x?
3) |x| = 25, what is/are x?
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1.7: Solve Absolute Value Equations

4. 1.7: Solve Absolute Value Equations
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More Quick Examples
|π – 3|
|3 – π|
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5. 1.7: Solve Absolute Value Equations
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Steps
Isolate the absolute value equation
Write two equations, with one answer being positive and other is negative
Solve each equation
Check by plugging each solution and make sure there aren’t any extraneous solutions
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6. 1.7: Solve Absolute Value Equations
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Example 1
Solve |x – 4| = 9 and list any extraneous solutions.
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7. 1.7: Solve Absolute Value Equations
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Example 2
Solve |2x + 12| = 4x and list any extraneous solutions.
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8. 1.7: Solve Absolute Value Equations
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Your Turn
Solve |4x – 1| = 2x + 9 and list any extraneous solutions
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9. 1.7: Solve Absolute Value Equations
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Example 3
Solve |2x + 5| – 3 = 8 and list any extraneous solutions
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10. 1.7: Solve Absolute Value Equations
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Example 4
Solve 2|x + 1| = 14 and list any extraneous solutions.
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11. 1.7: Solve Absolute Value Equations
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Your Turn
Solve 8|3x – 10| – 12 = 20 and list any extraneous solutions.
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12. 1.7: Solve Absolute Value Equations
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Example 5
Solve |x + 4| = 3x – 8 and list any extraneous solutions.
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13. 1.7: Solve Absolute Value Equations
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Example 6
Solve |3x + 1| = |2x + 3| and list any extraneous solutions.
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14. 1.7: Solve Absolute Value Equations
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Your Turn
Solve |x + 1| = |x – 1| and list any extraneous solutions.
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15. 1.7: Solve Absolute Value Equations
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Example 7
Solve |3x – 1|= 0 and list any extraneous solutions.
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16. 1.7: Solve Absolute Value Equations
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Example 8
Solve |5x – 1| = –2 and list any extraneous solutions.
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17. 1.7: Solve Absolute Value Equations
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Example 9
Solve –2|x + 1| = 14 and list any extraneous solutions.
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18. 1.7: Solve Absolute Value Equations
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Your Turn
Solve |x + 1| = |x – 1| and list any extraneous solutions.
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19. 1.7: Solve Absolute Value Equations
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Example 10
Solve |x| + |x + 3| = 3 and list any extraneous solutions
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20. 1.7: Solve Absolute Value Equations
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Your Turn
Solve |x| + |x – 5| = 5 and list any extraneous solutions.
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21. 1.7: Solve Absolute Value Equations
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Assignment
Absolute Value Worksheet A
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