**Solution:**

To find the value of *k* when *x* = -1/2 is a solution of the quadratic equation 3x² + 2kx - 3 = 0, we can substitute *x* = -1/2 into the equation and solve for *k*.

**Step 1: Substitute the value of x into the equation**

Substituting *x* = -1/2 into the equation, we have:

3(-1/2)² + 2k(-1/2) - 3 = 0

Simplifying the equation further, we get:

3(1/4) - k/2 - 3 = 0

3/4 - k/2 - 3 = 0

**Step 2: Simplify the equation**

To simplify the equation, we need to find a common denominator for the fractions. The common denominator here is 4.

Multiplying the fractions by their respective denominators to eliminate the fractions, the equation becomes:

3(1/4) - 2k/4 - 12/4 = 0

3/4 - 2k/4 - 12/4 = 0

**Step 3: Combine like terms**

Combining the like terms in the equation, we have:

(3 - 2k - 12)/4 = 0

-2k - 9 = 0

**Step 4: Solve for k**

To solve for *k*, we isolate it on one side of the equation.

Adding 9 to both sides of the equation, we get:

-2k = 9

Dividing both sides of the equation by -2, we have:

k = -9/2

Therefore, the value of *k* when *x* = -1/2 is a solution of the quadratic equation 3x² + 2kx - 3 = 0 is -9/2.