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- 2. ABSOLUTE VALUE Absolute Value: refers to a distance a from a certain quantity. Absolute Value Equation: It means that or
- 4. WAYS OF SOLVING ABSOLUTE VALUE EQUATIONS 1. Number-line Method – done by finding the center and endpoints of an absolute value equation. For instance, |x-a| =b A. Center: x-a=0;x=a B. Endpoints: a+b, a-b 2. Algebraic Method – done by using the definition of Absolute Value Equations in which the concept of disjunction will be applied.
- 5. STEPS IN SOLVING ABSOLUTE VALUE EQUATIONS: 1.Isolate the absolute value on one side of the equation. 2.Is the number on the other side of the equation negative? Yes – No Solution No – Proceed to step 3 3.Write two equations without absolute values. Equation 1 – Positive Equation 2 – Negative 4.Solve the two equations.
- 6. EXAMPLE
- 9. 1.
- 10. 2.
- 12. ABSOLUTE VALUE INEQUALITY Absolute Value Inequality – is an inequality involving an absolute value that can be written as combined inequality containing either, and, or or.
- 13. AVLT AND AVGT Absolute Value Less Than (AVLT): |x|<a, where x is a polynomial and a is a real number. This means that x<a and x>-a. Furthermore, it can be interpreted that the values of x are less than a units from the origin. Absolute Value Greater Than (AVGT): |x|>a, where x is a polynomial and a is a real number. This means that x>a and x<-a. Furthermore, it can be interpreted that the values of x are more than a units from the origin.
- 14. SOLVING ABSOLUTE VALUE INEQUALITIES 1. Isolate the inequality. 2. Identify whether the given absolute inequality is an AVLT or an AVGT. 3. For AVLT – Conjunction (uses ‘and’) For AVGT – Disjunction (uses ‘or’) 4. It will be further solved by applying the different properties of inequalities. 5. Write the solution set. 6. Graph the solution set.
- 15. Types of Absolute Value Inequality Less Than Less than equal to Greater Than Greater Than Equal to Zero No Solution Equate absolute Value to Zero then Solve (only 1 solution) All Real numbers except for the numbers that make it zero. All real numbers Negative No Solution No Solution All Real Numbers All Real Numbers Positive Create a 3-part Create a 3-part Create a 3-part Create a 3-part
- 16. EXAMPLE 1 Type: Greater than or equal to a positive number
- 17. EXAMPLE 2: LESS THAN A POSITIVE NUMBER
- 18. EXAMPLE 3: LESS THAN A NEGATIVE NUMBER
- 19. GREATER THAN OR EQUAL TO A NEGATIVE NUMBER
- 21. LESS THAN EQUAL TO NEGATIVE NUMBER
- 22. EXAMPLE
- 23. PRACTICE 1. 2.
- 24. ABSOLUTE VALUE WORD PROBLEMS
- 25. STEPS IN SOLVING WORD PROBLEMS 1. Understand the problem 2. Plan Your approach 3. Complete the work 4. Interpret the results
- 26. EXAMPLE 1 Bottles manufactured in a factory must be 250 ml in volume with a tolerance of 20 ml. Bottles that are not within the tolerated volume cannot be sold. What is the range of volume? (x is the volume of the bottle).
- 27. EXAMPLE 2 The weight of each fountain pen manufactured in a factory must be 10g with a tolerance of 2g. Pens that are not within the tolerated weight must be thrown away. What is the range of the allowable weight of a fountain pen? (x is the weight of the pen).