What exactly is this equation?

Question

Thank you for assistance, I'm just having issues remembering what this is called? For example, the equation would go like this

|x+1| = 4

What is this type of equation called, with the two | | ?

Thanks!

P.s I had no idea what tag to put it under!

Answer 1

$|x|$ is the absolute value of $x$. If $x$ is a real number, then $|x|$ is simply $x$ with the potential minus sign removed. In other words, if $x<0$, then $|x|=-x$, and if $x>0$, then $|x|=x$.

Answer 2

They are the absolute value sign. Also called the magnitude or norm.

$$\forall x \in \Bbb R:\quad \lvert x\rvert = \begin{cases} \quad x & : x\geq 0 \\ \,-x & : x< 0\end{cases}$$

For complex numbers, $\lvert a+b\imath\rvert = {+}\sqrt{a^2+b^2}$, where $a,b$ are the real and imaginary components of the number.

Answer 3

The notation $|x|$ is read aloud as "the absolute value of $x$", and is defined to be one of the two following things:

• If $x$ is non-negative, then $|x| = x$
• If $x$ is negative, then $|x| = -x$.

Informally, absolute value "throws away" negative signs; slightly more precisely, it turns negative numbers into positive numbers, and otherwise does nothing.

$|x|$ can also be interpreted as the distance of $x$ from $0$. It is also sometimes called the "magnitude" of $x$.

Answer 4

The symbol $|a-b|$ denotes the distance between the two numbers $a$ and $b$.

If you write the equation $|x+1| = 4$ as $$|x - (-1)| = 4$$ then you want to find the number $x$ such that the distance between it and $(-1)$ is equal to $4$. If you draw a number line, you will see that the numbers $3$ and $(-5)$ are at a distance of $4$ from the number $(-1)$ .