# 1) absolute value 2) empty set Evaluate expressions involving absolute values. Solve absolute value equations. Solving Absolute Value Equations

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Slide 2 1) absolute value 2) empty set Evaluate expressions involving absolute values. Solve absolute value equations. Solving Absolute Value Equations Slide 3 Seismologists use the Richter scale to express the Magnitudes of earthquakes. This scale ranges from 1 to 10, 10 being the highest. The uncertainty in the estimate of a magnitude E is about Plus or minus 0.3 unit. Richter Scale 0 10 E This means that an earthquake with a magnitude estimated at 6.1 might actually have a magnitude as low as 5.8 or as high as 6.4. These extremes can be described by the absolute value equation Slide 4 The absolute value of a number is its distance from zero on the number line. Since distance is nonnegative (positive), the absolute value of a number is always nonnegative. Solving Absolute Value Equations Slide 5 The absolute value of a number is its distance from zero on the number line. Since distance is nonnegative (positive), the absolute value of a number is always nonnegative. The symbol is used to represent the absolute value of a number x. Solving Absolute Value Equations Slide 6 Absolute Value For any real number a,if a is positive or zero,the absolute value of a is a. 0 a distance from zero = a distance from zero = a For any real number a,if a is negative,the absolute value of a is a. -a For any real number a, and Solving Absolute Value Equations Slide 7 Slide 8 negative side: positive side: Slide 9 Solving Absolute Value Equations negative side: positive side: Solution set is: { 8, 42 } Slide 10 Solving Absolute Value Equations Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3. Slide 11 Solving Absolute Value Equations Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3. Slide 12 Solving Absolute Value Equations negative side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3. Slide 13 Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3. Slide 14 Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3. Slide 15 Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3. Slide 16 Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3. Slide 17 Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3. Slide 18 Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3. Slide 19 Solving Absolute Value Equations Step 1) Isolate the absolute value expression by dividing both sides of the equation by 12. Absolute values are all NONNEGATIVE! Slide 20 Solving Absolute Value Equations Step 1) Isolate the absolute value expression by dividing both sides of the equation by 12. Absolute values are all NONNEGATIVE! This is referred to as an EMPTY SET.

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