Step 1: Simplify the equation
First, we need to simplify the given equation by combining like terms.
5x + 7/2 = 3/2x - 14
To get rid of the fractions, we can multiply every term by 2 to clear the denominators:
10x + 7 = 3x - 28

Step 2: Rearrange the equation
Next, we can rearrange the equation to isolate the variable on one side:
10x - 3x = -28 - 7
7x = -35

Step 3: Solve for x
Now, we can solve for x by dividing both sides by 7:
x = -35/7
x = -5

Step 4: Check the solution
Finally, we should substitute the value of x back into the original equation to verify if it satisfies the equation:
5(-5) + 7/2 = 3/2(-5) - 14
-25 + 7/2 = -15/2 - 14
-25 + 3.5 = -7.5 - 14
-21.5 = -21.5
Since both sides are equal, the solution x = -5 is correct.