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**Solving Absolute Value Equations**

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**Vocabulary Solving Absolute Value Equations**

Evaluate expressions involving absolute values. Solve absolute value equations. Vocabulary 1) absolute value 2) empty set

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**Solving Absolute Value Equations**

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. 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 Richter Scale 10 E

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**Solving Absolute Value Equations**

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.

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**Solving Absolute Value Equations**

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. is used to represent the absolute value of a number x. The symbol

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**Solving Absolute Value Equations**

For any real number a, if a is positive or zero, the absolute value of a is a. For any real number a, if a is negative, the absolute value of a is a. distance from zero = a distance from zero = a -a a For any real number a, and

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**Solving Absolute Value Equations**

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**Solving Absolute Value Equations**

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**

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

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**Solving Absolute Value Equations**

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

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**Solving Absolute Value Equations**

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

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**Solving Absolute Value Equations**

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

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**Solving Absolute Value Equations**

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

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**Solving Absolute Value Equations**

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

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**Solving Absolute Value Equations**

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

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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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Section 2.7 Absolute Value Equations and Inequalities.

Section 2.7 Absolute Value Equations and Inequalities.

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