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Absolute Value

Something Easier. Absolute value.

The notation for Absolute value is |a| . Note that a \in R .

|a| represents a when a>0 , 0 when a=0 and lastly -a when a<0 .

Absolute value is defined as the geometric distance from a to 0.

Basically, when solving Absolute Value equations, you must split up the possibilities and consider all cases as to what a can be, substitute the solutions back into the equation and see what works.

Cool fact: \sqrt{x^2} = |x| . Usually, we go straight to \sqrt{4}=2 , which is actually |2|=2 .

However, the absolute value is important as x might take a negative value.

Try:

Solve for x here: 3|x| + 2|x| - 1 = 0

and

Find all possible values of this: \displaystyle{\frac{x}{|x|} + \frac{y}{|y|}} .

Thx,

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