Absolute value around numbers Example: $y = 2|x + 2|$

Question

I know this is a super basic question but I can't find an answer. Is it that the result of anything within the absolute value, $|\,|$, must be evaluated first and given a positive value?

I knew this years ago but I've forgotten. So for... \begin{align*} y & = 2|x + 2|, \quad \text{where }x = -3\\ \Rightarrow \quad y & = 2. \end{align*}

Correct?

Answer 1

Yes, you must first evaluate the value of expression in the || (which named absolute) and then if the value is negative multiply it by -1

see here for more information.

Answer 2

Yes, you must evaluate what is inside of the absolute value symbols first, and then just use the magnitude of that value.

Hence, in algebra, say,$$|x + 2| = \frac{y}{2}$$can have two possibilities:$$x + 2 = \frac{y}{2}$$and$$-x - 2 = \frac{y}{2}.$$

Be careful of this you must. (This wasn't your question, but I thought that this point was important to address.)