Absolute Value Equations (Algebra 2)

1) absolute value2) empty set

Evaluate expressions involving absolute values.

Solve absolute value equations.

Solving Absolute Value Equations Solving Absolute Value Equations

Solving Absolute Value Equations 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.

Solving Absolute Value Equations 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 aboutPlus or minus 0.3 unit.

Solving Absolute Value Equations 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 aboutPlus or minus 0.3 unit.

This means that an earthquake with a magnitude estimatedat 6.1 might actually have a magnitude as low as 5.8 or ashigh as 6.4.

Solving Absolute Value Equations 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 aboutPlus or minus 0.3 unit.

This means that an earthquake with a magnitude estimatedat 6.1 might actually have a magnitude as low as 5.8 or ashigh as 6.4.

These extremes can be described by the absolute value equation 3.01.6 E

Solving Absolute Value Equations 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 aboutPlus or minus 0.3 unit.

Richter Scale

0 10

E

This means that an earthquake with a magnitude estimatedat 6.1 might actually have a magnitude as low as 5.8 or ashigh as 6.4.

These extremes can be described by the absolute value equation 3.01.6 E

The absolute value of a number is its distance from zero on the number line.

Solving Absolute Value Equations 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 alwaysnonnegative.

Solving Absolute Value Equations 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 alwaysnonnegative.

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

Solving Absolute Value Equations Solving Absolute Value Equations

Absolute Value

For any real number a, if a is positive or zero, the absolute value of a is a.

Solving Absolute Value Equations Solving Absolute Value Equations

Absolute Value

For any real number a, if a is positive or zero, the absolute value of a is a.

0 a

distance fromzero = a

Solving Absolute Value Equations Solving Absolute Value Equations

Absolute Value

For any real number a, if a is positive or zero, the absolute value of a is a.

0 a

distance fromzero = a

distance fromzero = a

For any real number a, if a is negative, the absolute value of a is a.

-a

Solving Absolute Value Equations Solving Absolute Value Equations

Absolute Value

For any real number a, if a is positive or zero, the absolute value of a is a.

0 a

distance fromzero = a

distance fromzero = a

For any real number a, if a is negative, the absolute value of a is a.

-a

For any real number a, ,0 if aaa .0 if and aaa

Solving Absolute Value Equations Solving Absolute Value Equations

Absolute Value

For any real number a, if a is positive or zero, the absolute value of a is a.

0 a

distance fromzero = a

distance fromzero = a

For any real number a, if a is negative, the absolute value of a is a.

-a

For any real number a, ,0 if aaa .0 if and aaa

33 and33

Solving Absolute Value Equations Solving Absolute Value Equations

Solving Absolute Value Equations Solving Absolute Value Equations

8265 if ,expression theEvaluate . c, and , ba

aa 2103

Solving Absolute Value Equations Solving Absolute Value Equations

8265 if ,expression theEvaluate . c, and , ba

aa 2103 521053

Solving Absolute Value Equations Solving Absolute Value Equations

8265 if ,expression theEvaluate . c, and , ba

aa 2103 521053

10153

Solving Absolute Value Equations Solving Absolute Value Equations

8265 if ,expression theEvaluate . c, and , ba

aa 2103 521053

10153

10153

Solving Absolute Value Equations Solving Absolute Value Equations

8265 if ,expression theEvaluate . c, and , ba

aa 2103 521053

10153

10153

1045

Solving Absolute Value Equations Solving Absolute Value Equations

8265 if ,expression theEvaluate . c, and , ba

aa 2103 521053

10153

10153

1045

55

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

1725 x

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

1725 x

1725 x

negative side:

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

1725 x

1725 x

negative side: positive side:

1725 x

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

1725 x

1725 x

negative side: positive side:

1725 x

8x

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

1725 x

1725 x

negative side: positive side:

1725 x

8x 42x

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

1725 x

1725 x

negative side: positive side:

1725 x

8x 42x

Solution set is: { 8, 42 }

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

123723 zz

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

123723 zz

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

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

123723 zz

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

472 zz

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

123723 zz

)4(72 zz

negative side:

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

472 zz

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

123723 zz

)4(72 zz

negative side: positive side:

472 zz

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

472 zz

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

123723 zz

)4(72 zz

negative side: positive side:

472 zz

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

472 zz

472 zz

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

123723 zz

)4(72 zz

negative side: positive side:

472 zz

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

472 zz

472 zz

742 zz

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

123723 zz

)4(72 zz

negative side: positive side:

472 zz

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

472 zz

472 zz

742 zz

113 z

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

123723 zz

)4(72 zz

negative side: positive side:

472 zz

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

472 zz

472 zz

742 zz

113 z

3

11z

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

123723 zz

)4(72 zz

negative side: positive side:

472 zz

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

472 zz

472 zz 742 zz

742 zz

113 z

3

11z

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

123723 zz

)4(72 zz

negative side: positive side:

472 zz

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

472 zz

472 zz 742 zz

742 zz 3z

113 z

3

11z

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

123723 zz

)4(72 zz

negative side: positive side:

472 zz

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

472 zz

472 zz 742 zz

742 zz 3z

113 z

3

11z

3 ,

3

11 :isset Solution

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

481912 x

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

481912 x

Step 1) Isolate the absolute value expression by dividing both sides of the equation by – 12.

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

481912 x

Step 1) Isolate the absolute value expression by dividing both sides of the equation by – 12.

419 x

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

481912 x

Step 1) Isolate the absolute value expression by dividing both sides of the equation by – 12.

419 x

Absolute values are all NONNEGATIVE!

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

481912 x

Step 1) Isolate the absolute value expression by dividing both sides of the equation by – 12.

419 x

Absolute values are all NONNEGATIVE!

:isset Solution

Solving Absolute Value Equations Solving Absolute Value Equations

solution.your Check equation. theSolve

481912 x

Step 1) Isolate the absolute value expression by dividing both sides of the equation by – 12.

419 x

Absolute values are all NONNEGATIVE!

:isset Solution

This is referred to as an EMPTY SET.

Basic Absolute Value

Absolute Value EquationOffset from Zero

Solving Absolute Value Equations Solving Absolute Value Equations

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Using Glencoe’s Algebra 2 text,© 2005

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