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

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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

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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

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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

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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

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negative side: positive side:

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Solving Absolute Value Equations negative side: positive side: Solution set is: { 8, 42 }

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Solving Absolute Value Equations Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3.

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Solving Absolute Value Equations Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3.

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Solving Absolute Value Equations negative side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3.

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Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3.

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Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3.

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Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3.

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Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3.

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Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3.

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Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3.

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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!

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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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