First, we can simplify the absolute values on both sides of the equation:

|−0.63| ÷ |x| = |−0.91|

This simplifies to:

0.63 ÷ |x| = 0.91

Now, we need to solve for x. We can start by multiplying both sides of the equation by |x| to get rid of the division:

0.63 = 0.91|x|

Next, we can divide both sides by 0.91 to solve for |x|:

|x| = 0.63 / 0.91
|x| = 0.6923

Since |x| is the absolute value of x, x can be either positive or negative. Therefore, x can be either 0.6923 or -0.6923.