To solve the equation, we need to simplify both sides and isolate the variable.

Starting with the left side of the equation:

-1/2 - x

To combine the terms, we need a common denominator. The common denominator for 2 and 3 is 6.

-1/2 can be written as -3/6, and x remains the same.

So, the left side becomes:

-3/6 - x

Now, let's simplify the right side of the equation:

1/3 - 1/-4

To combine the terms, we need a common denominator. The common denominator for 3 and 4 is 12.

1/3 can be written as 4/12, and 1/-4 can be written as -3/12.

So, the right side becomes:

4/12 - (-3/12)

Simplifying further:

4/12 + 3/12

Combining the terms:

7/12

Now, the equation becomes:

-3/6 - x = 7/12

To isolate x, we can start by getting rid of the fraction on the left side. We can do this by multiplying both sides of the equation by 12:

12 * (-3/6 - x) = 12 * (7/12)

Simplifying:

-6 - 12x = 7

Next, we can move the constant term to the other side of the equation by adding 6 to both sides:

-6 + 6 - 12x = 7 + 6

Simplifying:

-12x = 13

Finally, we can solve for x by dividing both sides of the equation by -12:

(-12x)/-12 = 13/-12

Simplifying:

x = -13/12

Therefore, the solution to the equation is x = -13/12.