Solving Absolute Value Equations

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Solving Absolute-Value Equations

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Solving Absolute Value Equations

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Presentation transcript:

Solving Absolute Value Equations

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

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

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.

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

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

Solving Absolute Value Equations

Solving Absolute Value Equations negative side: positive side:

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

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

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

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

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

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

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

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

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

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

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!

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.