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1.6 ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

# 1.6 Absolute Value Equations and Inequalities

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• 1. 1.6 ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

2. ABSOLUTE VALUE

• Theabsolute valueof a real numberx , written | x |, is its distance from zero on the number line
• Example: |5| = 5
• |-5| = 5

3. ABSOLUTE VALUES EQUATION

• Anabsolute value equationis an equation that has a variable inside the absolute value sign
• Absolute value equations can have two answers because opposites have the same absolute value.

4. SOLVING ABSOLUTE VALUE EQUATIONS

• To solve an absolute value equation:
• Isolate the absolute value
• remove the absolute value signs and set up as shown:

5. SOLVE EACH EQUATION. GRAPH THE SOLUTION. 6. SOLVE EACH EQUATION. GRAPH THE SOLUTION. 7. SOLVE EACH EQUATION. GRAPH THE SOLUTION. 8. SOLVE EACH EQUATION. GRAPH THE SOLUTION. 9. EXTRANEOUS SOLUTIONS

• Anextraneous solutionis a solution derived from an original equation that isnota solution of the original equation.
• Remember that the absolute value measures the distance from zero on a number line. Distance can never be negative. Therefore, we must check our answers when working with absolute values.

10. SOLVE AND CHECK FOR EXTRANEOUS SOLUTIONS. 11. SOLVE AND CHECK FOR EXTRANEOUS SOLUTIONS. 12. SOLVE AND CHECK FOR EXTRANEOUS SOLUTIONS. 13. ABSOLUTE VALUE INEQUALITIES

• Anabsolute value inequalityis an inequality that has a variable inside the absolute value sign.

14. SOLVING ABSOLUTE VALUE INEQUALITIES

• Write the absolute value inequality as a compound inequality without absolute value symbols

15. 16. SOLVE AND GRAPH THE SOLUTION. 17. SOLVE AND GRAPH THE SOLUTION. 18. SOLVE AND GRAPH THE SOLUTION.

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