Absolute Value Equations and Inequalities Flashcards

Question 1

What is the definition of absolute value $|x|$?

Accepted Answer

$$|x|=\begin{cases}x,&x\ge 0\-x,&x<0\end{cases}$$ It represents the distance of $x$ from $0$ on the number line.

Question 2

State the inequality rule equivalent to $|x|<a$ (with $a>0$).

Accepted Answer

$$|x|<a \iff -a<x<a \quad (a>0)$$

Question 3

How do you graph $y=|x|$ and what is its general shape?

Accepted Answer

It is a V-shape with vertex at $(0,0)$: $y=x$ for $x\ge 0$ and $y=-x$ for $x<0$.

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