Just how far from zero are you? Absolute Value Just how far from zero are you?

What are opposites on a number line? Graph the integer set from –5 to + 5 Two numbers that are the same distance from zero are said to be opposites

But what is Absolute Value? Absolute Value is the distance a number is from zero. Remember distance itself is ALWAYS positive

How do we denote absolute value? SO let’s try a few: What general statement can you make about absolute value?

Be careful! In math a negative sign in front of the absolute value sign should be read “take the opposite of”. This means treat the absolute value sign like a grouping symbol. Do the work inside first THEN take the opposite of

Let’s try a few

What if the variable is in the absolute value sign? This simply means what are ALL the solutions that make this a true statement? -7 7

Velocity and Speed Velocity is how fast is something going AND in what direction is it headed? Example: If I am plummeting to earth in a hot air balloon my velocity would be –15 feet per second! BUT my speed would be the absolute value which is?

THINK ABOUT IT… In math it is not enough to just know the answer you have to PROVE you know it. If you say something is FALSE you must provide a counter example. Give a counter example to this statement: All of the students in Mrs. Rose’s algebra classes are boys. Now determine if these are true or false. If false, provide a counter example: The expression – x is never positive The absolute value of a number will always be greater than or equal to that number