The expression of the variable z in the equation is z = v - x - y - 14, using the balance method.
To solve the equation for z in the equation x + y + z + 14 = v, we subtract all the terms without z from both sides of the equation to solve for the variable z as follows;
x + y + z + 14 = v
subtract x from both sides;
x - x + y + z + 14 = v - x
y + z + 14 = v - x
subtract y from both sides;
y - y + z + 14 = v - x - y
z + 14 = v - x - y
subtract 14 from both sides;
z + 14 - 14 = v - x - y - 14
z = v - x - y - 14.
Therefore, after solving for z using the balance method, we have it as: z = v - x - y - 14.