# 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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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. Slide 2 Graphing Absolute Value X = 6 Where are the numbers that are 6 units from zero? 20315476-4-2-3-5-6-720315476-4-2-3-5-6-7 Graph: OR { 6, -6} Slide 3 Graphing Absolute Value X 3 Where are the numbers that are more than 3 units from zero? 20315476-4-2-3-5-6-7 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 Slide 4 Graphing Absolute Value X 3 Where are the numbers that are less than 3 units from zero? 20315476-4-2-3-5-6-7 Graph: To the left of 3 To the right of -3 Do you want the 3? Yes Do you want the -3? Yes 20315476-4-2-3-5-6-7 AND at the same time -3 X 3 Slide 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 Slide 6 -1(X)= 3 X =-3 0 -5-4-3-212345 0 -5-4-3-212345 0 -5-4-3-212345 B A B Put together A X = 3 If X > 0 X = 3 or If X< 0 -(X)= 3 A B { 3, -3} Slide 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 # Slide 8 -1(X) 4 X -4 0 -5-4-3-212345 0 -5-4-3-212345 0 -5-4-3-212345 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 Slide 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 Slide 10 -1(X) 2 X -2 0 -5-4-3-212345 0 -5-4-3-212345 0 -5-4-3-212345 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 Slide 11 OR = Positive # - ( ) = Positive # OR > Positive # - ( ) > Positive # AND < Positive # - ( ) < Positive # Slide 12 2X -3 > 1 or -(2X -3) > 1 -2X +3 > 1 -2 X 2 -3 -3 -2X > -2 IF YOU MULTIPLY OR DIVIDE BOTH SIDES OF AN INEQUALITY BY A NEGATIVE TURN THE INEQUALITY SIGN AROUND > X 2 Slide 13 5X -3 = 7 or -(5X -3) = 7 -5X +3 = 7 -5 X = -.8 0 -5-4-3-212345 0 -5-4-3-212345 0 -5-4-3-212345 B A B Put together ? A A B +3 5X10 55 X = 2 -3 -3 -5X = 4 = { 2, -.8} Slide 14 3X +6 9 and -(3X +6) 9 -3X - 6 9 -3 X -5 0 -4-3-212345 0 -5-4-3-212345 0 -5-4-3-212345 B A B Whats the same? A A B -6 3X3 33 X 1 +6 +6 -3X 15 -5 X 1 Slide 15 Graphing Absolute Value 2X - 3 = - 6 Absolute value is always a positive number or zero. 20315476-4-2-3-5-6-7 Graph: Absolute value will never equal a negative number. NO SOLUTION Slide 16 Graphing Absolute Value X - 5 < -2 Absolute value is always a positive number or zero. 20315476-4-2-3-5-6-7 Graph: Since absolute value is always positive or zero, it cannot be less than a negative number. NO SOLUTION Slide 17 Graphing Absolute Value 3X+2 -2 Absolute value is always a positive number or zero. 20315476-4-2-3-5-6-7 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 Slide 18 ABSOLUTE VALUE 0 -5-4-3-212345 SYMBOL: Distance from zero OPPOSITES or ADDITIVE INVERSES Have the same absolute value -2 = 2 2 = 2 -1.51.5

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