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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