Post on 27-Mar-2015
transcript
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.
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.
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.
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 521053
10153
10153
55
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
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 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
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.