Question

For an absolute value equation, there are two solutions. Use the given equation and it’s solutions to algebraically prove this statement to be true |x|=9 (show work so I understand how to do it as well please!!)

Answer 1

The first sentence is not true in general. Consider the equation $|x|=-1$. There are no solutions. Now consider $|x|=0$. There is only one solution, $x=0$.

But whatever. You're asked to demonstrate that $|x|=9$ has two solutions (which is true; the right hand side must be a positive integer in order to have two solutions). This follows immediately from the definition of absolute value, which says

$|x|=\begin{cases}x&\text{for }x\ge0\\-x&\text{for }x$

So suppose $x\ge0$. Then

$|x|=9\implies x=9$

Now suppose $x$. Then

$|x|=9\implies -x=9\implies x=-9$

So two solutions to $|x|=9$ are $x=\pm9$.

Answer 2

X = 9 or -9 
this is true because absolute value means the distance from 0 and on a number line it takes 9 jumps to get from 9 and -9.