Let's solve the equation step by step.

Starting from:

\[
|x| = \frac{3}{2}
\]

The absolute value equation can be broken down into two cases:

1. \( x = \frac{3}{2} \)
2. \( x = -\frac{3}{2} \)

Therefore, the solutions for \( |x| = \frac{3}{2} \) are:

\[
x = \frac{3}{2} \quad \text{and} \quad x = -\frac{3}{2}
\]

If you meant the equation \( \frac{3}{2|x|} = \frac{3}{2} \), we can also solve it as follows:

Multiply both sides by \( 2|x| \):

\[
3 = 3|x|
\]

Dividing both sides by \( 3 \) results in:

\[
1 = |x|
\]

Again, this leads us to two cases:

1. \( x = 1 \)
2. \( x = -1 \)

So, depending on the interpretation of your original equation, we have either:

1. \( |x| = \frac{3}{2} \) leading to \( x = \frac{3}{2} \) or \( x = -\frac{3}{2} \)
2. \( \frac{3}{2|x|} = \frac{3}{2} \) leading to \( x = 1 \) or \( x = -1 \)

Please clarify if you had a different equation in mind!