To solve this equation, we need to find the sum of the given series.

Let's break down the series into individual terms:

x - 3/1 + 2 - 3/2 + 2 - 3/3 + 4 - ...

We can see that the pattern is as follows:

Term 1: x
Term 2: -3/1 + 2
Term 3: -3/2 + 2
Term 4: -3/3 + 4
...

To find the sum of the series, we can start by simplifying each term:

Term 1: x
Term 2: -3/1 + 2 = -3 + 2 = -1
Term 3: -3/2 + 2 = -1.5 + 2 = 0.5
Term 4: -3/3 + 4 = -1 + 4 = 3
...

Now, let's write out the series with the simplified terms:

x - 1 + 0.5 + 3 + ...

To find the sum of this series, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

where S is the sum, a is the first term, and r is the common ratio.

In this case, the first term (a) is x, and the common ratio (r) is -0.5 (each term is multiplied by -0.5 to get the next term).

So, the sum of the series is:

S = x / (1 - (-0.5))
S = x / (1 + 0.5)
S = x / 1.5

Now, we are given that the sum of the series is -1:

x / 1.5 = -1

To solve for x, we can multiply both sides of the equation by 1.5:

x = -1 * 1.5
x = -1.5

Therefore, the value of x that satisfies the equation is -1.5.