The solution to the absolute value equation "0 = |u - 9|" is "u = 9", as the absolute value of any real number is zero when the number itself is zero.
The equation "0 = |u - 9|" represents an absolute value equation, where the expression "|u - 9|" denotes the distance between "u" and 9 on the number line. The absolute value function returns non-negative values, so for the equation to hold true, the expression "|u - 9|" must equal zero.
The only way for the absolute value of an expression to be zero is if the expression inside the absolute value bars is zero. Therefore, "u - 9 = 0". Solving this equation for "u", we add 9 to both sides to isolate "u":
u - 9 + 9 = 0 + 9
This simplifies to "u = 9".
So, the solution to the equation "0 = |u - 9|" is "u = 9".