Question

What is the answer for |x|=9

Answer 1

The absolute value $|x|$ returns the "positive version" of a number.

In other words, if the number is positive, it remains positive; if the number is negative, it changes sign.

So, if we want $|x|=9$, we want the "positive version" of x to be 9.

This can happen in two ways: if x is already 9, then its absolute value is still nine. If instead x=-9, its positive value will be 9 again.

In formula, we have

$|x|=9 \iff x=\pm 9$

because

$|9|=9,\quad |-9|=9$