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

1) absolute value2) empty set

Evaluate expressions involving absolute values.

Solve 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.

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.

Since distance is nonnegative (positive), the absolute value of a number is alwaysnonnegative.


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.


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



8265 if ,expression theEvaluate . c, and , ba

aa 2103 521053

10153

10153

55


solution.your Check equation. theSolve

1725 x

1725 x

negative side: positive side:

1725 x

8x 42x



1725 x

1725 x


1725 x

8x 42x

Solution set is: { 8, 42 }



123723 zz

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



123723 zz


472 zz



123723 zz

)4(72 zz

negative side:


472 zz



123723 zz

)4(72 zz


472 zz


472 zz



123723 zz

)4(72 zz


472 zz


472 zz

472 zz



123723 zz

)4(72 zz


472 zz


472 zz

472 zz

742 zz



123723 zz

)4(72 zz


472 zz


472 zz

472 zz

742 zz

113 z



123723 zz

)4(72 zz


472 zz


472 zz

472 zz

742 zz

113 z

3

11z



123723 zz

)4(72 zz


472 zz


472 zz

472 zz 742 zz

742 zz 3z

113 z

3

11z

3 ,

3

11 :isset Solution



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



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.