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Absolute Value The absolute value of a number is its distance from zero. The symbol for absolute value is 6 = 6 -5 = 5 Absolute Value is always positive.

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Presentation on theme: "Absolute Value The absolute value of a number is its distance from zero. The symbol for absolute value is 6 = 6 -5 = 5 Absolute Value is always positive."— Presentation transcript:

1 Absolute Value The absolute value of a number is its distance from zero. The symbol for absolute value is 6 = 6 -5 = 5 Absolute Value is always positive or zero.

2 Graphing Absolute Value X = 6 Where are the numbers that are 6 units from zero? Graph: OR { 6, -6}

3 Graphing Absolute Value X 3 Where are the numbers that are more than 3 units from zero? Graph: To the right of 3 To the left of -3 Do you want the 3? NODo you want the -3?NO OR X 3

4 Graphing Absolute Value X 3 Where are the numbers that are less than 3 units from zero? Graph: To the left of 3 To the right of -3 Do you want the 3? Yes Do you want the -3? Yes AND at the same time -3 X 3

5 or = positive # If > 0 Could represent an expression that has a positive value or a negative value. = positive # If < 0 -( ) = positive # X = 3 If X > 0 X = 3 or If X< 0 -(X)= 3 A B An expression that represents any real number except 0

6 -1(X)= 3 X = B A B Put together A X = 3 If X > 0 X = 3 or If X< 0 -(X)= 3 A B { 3, -3}

7 or > positive # If > 0 Could represent an expression that has a positive value or a negative value. > positive # If < 0 An expression that represents any real number except 0 X 4 If X > 0 X 4 or If X< 0 -(X) 4 A B -( ) > positive #

8 -1(X) 4 X B A B Put together A X 4 or -(X) 4 A B IF YOU MULTIPLY OR DIVIDE BOTH SIDES OF AN INEQUALITY BY A NEGATIVE TURN THE INEQUALITY SIGN AROUND X 4

9 or < positive # If > 0 Could represent an expression that has a positive value or a negative value. < positive # If < 0 X 2 If X > 0 X 2 and If X< 0 -(X) 2 A B -( ) < positive # An expression that represents any real number except 0

10 -1(X) 2 X B A B Whats the same? A X 2 If X > 0 X 2 and If X< 0 -(X) 2 A B IF YOU MULTIPLY OR DIVIDE BOTH SIDES OF AN INEQUALITY BY A NEGATIVE TURN THE INEQUALITY SIGN AROUND -2 X 2

11 OR = Positive # - ( ) = Positive # OR > Positive # - ( ) > Positive # AND < Positive # - ( ) < Positive #

12 2X -3 > 1 or -(2X -3) > 1 -2X +3 > 1 -2 X < B A B Put together A A B +3 2X4 22 X> X > -2 IF YOU MULTIPLY OR DIVIDE BOTH SIDES OF AN INEQUALITY BY A NEGATIVE TURN THE INEQUALITY SIGN AROUND > X 2

13 5X -3 = 7 or -(5X -3) = 7 -5X +3 = 7 -5 X = B A B Put together ? A A B +3 5X10 55 X = X = 4 = { 2, -.8}

14 3X +6 9 and -(3X +6) 9 -3X X B A B Whats the same? A A B -6 3X3 33 X X X 1

15 Graphing Absolute Value 2X - 3 = - 6 Absolute value is always a positive number or zero Graph: Absolute value will never equal a negative number. NO SOLUTION

16 Graphing Absolute Value X - 5 < -2 Absolute value is always a positive number or zero Graph: Since absolute value is always positive or zero, it cannot be less than a negative number. NO SOLUTION

17 Graphing Absolute Value 3X+2 -2 Absolute value is always a positive number or zero Graph: Since absolute value is always positive or zero, it will ALWAYS be greater than ANY negative number. ALL Real Numbers will have an Absolute Value -2 R

18 ABSOLUTE VALUE SYMBOL: Distance from zero OPPOSITES or ADDITIVE INVERSES Have the same absolute value -2 = 2 2 =


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